Edit Profile (opens in new tab) Martini, Horst Co-Author Distance Author ID: martini.horst Published as: Martini, Horst; Martini, H. Homepage: https://www.tu-chemnitz.de/mathematik/geometrie/index.php External Links: MGP · Wikidata · dblp · GND · IdRef Documents Indexed: 299 Publications since 1984, including 6 Books and 3 Additional arXiv Preprints 2 Contributions as Editor Reviewing Activity: 483 Reviews Biographic References: 1 Publication Co-Authors: 78 Co-Authors with 266 Joint Publications 1,060 Co-Co-Authors all top 5 Co-Authors 33 single-authored 31 Spirova, Margarita Georgieva 28 Kupitz, Yaakov S. 28 Wu, Senlin 23 Balestro, Vitor 18 Makai, Endre jun. 16 Maehara, Hiroshi 15 Teixeira, Ralph Costa 14 Boltyanskij, Vladimir Grigor’evich 13 Mustafaev, Zokhrab 12 Hajja, Mowaffaq 12 Soltan, Valeriu 12 Swanepoel, Konrad J. 11 Perles, Micha A. 8 Alonso, Javier 8 Wenzel, Walter 6 Averkov, Gennadiy 6 He, Chan 6 Soltan, Petru 5 Horváth, Ákos G. 5 Richter, Christian 5 Schöbel, Anita 4 Jahn, Thomas 4 Lassak, Marek 4 Martín Jimenez, Pedro 4 Mozgawa, Witold 4 Shcherba, Anatoly I. 4 Weiß, Gunter 4 Weißbach, Bernulf 3 Cieślak, Waldemar 3 Edmonds, Allan L. 3 Geise, Gerhard 3 Ghandehari, Mostafa 3 Hansen, Guillermo L. 3 Ódor, Tibor 2 Hayajneh, Mostafa 2 Korneenko, Nikolai M. 2 Leopold, Undine 2 Nguyên Manh Hung 2 Papini, Pier Luigi 2 Sakaki, Makoto 2 Vincenzi, Giovanni 2 Wegner, Bernd 1 Anatriello, Giuseppina 1 Berele, Allan 1 Bordei, Alexei 1 Brandenberg, René 1 Catoiu, Stefan 1 Craizer, Marcos 1 de Wet, Pieter Oloff 1 Donisi, Serena 1 Gao, Laiyuan 1 Gao, Shenghua 1 González Merino, Bernardo 1 Hammoudeh, Ismail 1 Hansen, Gerd 1 Heil, Erhard 1 Herburt, Irmina 1 Hlibiciuc, Valentin 1 Ivanov, Grigory M. 1 Körner, Mark-Christoph 1 Krasopoulos, Panagiotis T. 1 Kuwata, Takayasu 1 Last, Hagit 1 Lv, Yafang 1 Montejano Peimbert, Luis 1 Moszyńska, Maria 1 Nam, Nguyen Mau 1 Nikonorov, Yurii Gennadyevich 1 Nikonorova, Yulia V. 1 Oliveros, Deborah 1 Pinchasi, Rom 1 Prisacaru, Kiril 1 Robinson, Adam 1 Schiel, Uwe 1 Schur, Zvi 1 Shonoda, Emad N. 1 Strambach, Karl 1 Talata, István 1 Vitale, Gaetano 1 Zhang, Deyan 1 Zhang, Longzhen all top 5 Serials 23 Beiträge zur Algebra und Geometrie 14 Results in Mathematics 13 Aequationes Mathematicae 9 Periodica Mathematica Hungarica 9 Geometriae Dedicata 9 Journal of Geometry 8 Studia Scientiarum Mathematicarum Hungarica 8 Journal of Convex Analysis 7 Discrete Mathematics 6 Colloquium Mathematicum 6 Acta Mathematica Hungarica 5 Archiv der Mathematik 5 Journal of Optimization Theory and Applications 5 Monatshefte für Mathematik 5 Discrete & Computational Geometry 5 Extracta Mathematicae 5 Elemente der Mathematik 5 Advances in Geometry 4 Rocky Mountain Journal of Mathematics 4 Acta Scientiarum Mathematicarum 4 Canadian Mathematical Bulletin 4 Expositiones Mathematicae 4 Mathematical Inequalities & Applications 3 American Mathematical Monthly 3 Discrete Applied Mathematics 3 Mathematische Semesterberichte 3 Journal of Graph Theory 3 Mathematika 3 Publicationes Mathematicae Debrecen 3 European Journal of Combinatorics 3 Note di Matematica 3 Graphs and Combinatorics 3 Applied Mathematics Letters 3 Computational Geometry 3 Mitteilungen der Mathematischen Gesellschaft in Hamburg 3 Journal for Geometry and Graphics 3 East-West Journal of Mathematics 3 Annals of Functional Analysis 2 Journal of Mathematical Analysis and Applications 2 The Mathematical Intelligencer 2 Journal of Combinatorial Theory. Series A 2 The Mathematics Student 2 Pacific Journal of Mathematics 2 Computer Aided Geometric Design 2 L’Enseignement Mathématique. 2e Série 2 Nieuw Archief voor Wiskunde. Vierde Serie 2 Congressus Numerantium 2 Studies in Locational Analysis 2 Ars Mathematica Contemporanea 2 Analysis and Mathematical Physics 1 Bulletin of the Australian Mathematical Society 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 The Mathematical Gazette 1 Revue Roumaine de Mathématiques Pures et Appliquées 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 1 Collectanea Mathematica 1 Czechoslovak Mathematical Journal 1 Quaestiones Mathematicae 1 Rendiconti del Seminario Matematico della Università di Padova 1 Utilitas Mathematica 1 Potsdamer Forschungen. Wissenschaftliche Schriftenreihe der Pädagogischen Hochschule ”Karl Liebknecht” Potsdam. Reihe B. Naturwissenschaftliche Reihe 1 JCMCC. The Journal of Combinatorial Mathematics and Combinatorial Computing 1 International Journal of Computational Geometry & Applications 1 Differential Geometry and its Applications 1 Irish Mathematical Society Bulletin 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Georgian Mathematical Journal 1 Journal of Inequalities and Applications 1 Annals of Combinatorics 1 DGDS. Differential Geometry – Dynamical Systems 1 Anale Ştiinţifice Facultatea de Matematică şi Informatică. Universitatea de Stat din Moldova 1 Contributions to Discrete Mathematics 1 Combinatorial Optimization 1 Journal of Mathematical Inequalities 1 Banach Journal of Mathematical Analysis 1 São Paulo Journal of Mathematical Sciences 1 Journal of Computational Geometry 1 Southeast Asian Journal of Sciences 1 Universitext 1 Birkhäuser Advanced Texts. Basler Lehrbücher 1 Cornerstones all top 5 Fields 234 Convex and discrete geometry (52-XX) 96 Geometry (51-XX) 84 Functional analysis (46-XX) 29 Differential geometry (53-XX) 16 Combinatorics (05-XX) 12 Operations research, mathematical programming (90-XX) 10 Computer science (68-XX) 9 History and biography (01-XX) 5 General and overarching topics; collections (00-XX) 5 Numerical analysis (65-XX) 4 Real functions (26-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Special functions (33-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Measure and integration (28-XX) 2 Approximations and expansions (41-XX) 2 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-XX) 2 Probability theory and stochastic processes (60-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 233 Publications have been cited 1,926 times in 899 Documents Cited by ▼ Year ▼ On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces. Zbl 1241.46006 Alonso, Javier; Martini, Horst; Wu, Senlin 122 2012 The geometry of Minkowski spaces – a survey. I. Zbl 0984.52004 Martini, Horst; Swanepoel, Konrad J.; Weiß, Gunter 119 2001 Excursions into combinatorial geometry. Zbl 0877.52001 Boltyanski, V.; Martini, H.; Soltan, Petru S. 110 1997 The geometry of Minkowski spaces – a survey. II. Zbl 1080.52005 Martini, H.; Swanepoel, K. J. 82 2004 Bodies of constant width. An introduction to convex geometry with applications. Zbl 1468.52001 Martini, Horst; Montejano, Luis; Oliveros, Déborah 68 2019 Geometric methods and optimization problems. Zbl 0933.90002 Boltyanski, V.; Martini, H.; Soltan, V. 65 1999 Antinorms and Radon curves. Zbl 1108.52005 Martini, Horst; Swanepoel, Konrad J. 57 2006 Combinatorial problems on the illumination of convex bodies. Zbl 0937.52006 Martini, Horst; Soltan, Valeriu 47 1999 Special convex bodies. Zbl 0794.52002 Heil, E.; Martini, H. 41 1993 Geometric aspects of the generalized Fermat-Torricelli problem. Zbl 0911.51021 Kupitz, Y. S.; Martini, H. 40 1997 The Fermat–Torricelli problem in normed planes and spaces. Zbl 1047.90032 Martini, H.; Swanepoel, K. J.; Weiss, G. 33 2002 Angles in normed spaces. Zbl 1365.52006 Balestro, Vitor; Horváth, Ákos G.; Martini, Horst; Teixeira, Ralph 22 2017 Reduced convex bodies in Euclidean space – a survey. Zbl 1213.52006 Lassak, Marek; Martini, Horst 20 2011 Orthogonality types in normed linear spaces. Zbl 1503.46009 Alonso, Javier; Martini, Horst; Wu, Senlin 19 2022 Ball polytopes and the Vázsonyi problem. Zbl 1224.52025 Kupitz, Y. S.; Martini, H.; Perles, M. A. 19 2010 Antipodality properties of finite sets in Euclidean space. Zbl 1066.52010 Martini, H.; Soltan, V. 17 2005 Hyperplane approximation and related topics. Zbl 0809.52013 Korneenko, Nikolai M.; Martini, Horst 16 1993 Minimal enclosing discs, circumcircles, and circumcenters in normed planes. I. Zbl 1245.65022 Alonso, Javier; Martini, Horst; Spirova, Margarita 15 2012 The Feuerbach circle and orthocentricity in normed places. Zbl 1144.52001 Martini, Horst; Spirova, Margarita 15 2007 Orthocentric simplices and their centers. Zbl 1084.51008 Edmonds, Allan L.; Hajja, Mowaffaq; Martini, Horst 15 2005 On the theorem of Napoleon and related topics. Zbl 0864.51009 Martini, Horst 14 1996 The cross-section body, plane sections of convex bodies and approximation of convex bodies. I. Zbl 0865.52005 Makai, E. jun.; Martini, H. 14 1996 Minimal enclosing discs, circumcircles, and circumcenters in normed planes. II. Zbl 1251.65016 Alonso, Javier; Martini, Horst; Spirova, Margarita 14 2012 Reduced convex bodies in finite dimensional normed spaces: a survey. Zbl 1310.52004 Lassak, Marek; Martini, Horst 14 2014 Reduced bodies in Minkowski space. Zbl 1084.52004 Lassak, M.; Martini, H. 14 2005 Median hyperplanes in normed spaces – a survey. Zbl 0921.90109 Martini, Horst; Schöbel, Anita 13 1998 Coincidences of simplex centers and related facial structures. Zbl 1093.51014 Edmonds, Allan L.; Hajja, Mowaffaq; Martini, Horst 13 2005 Starshaped sets. Zbl 1454.52001 Hansen, G.; Herburt, I.; Martini, H.; Moszyńska, M. 13 2020 Concepts of curvatures in normed planes. Zbl 1432.52001 Balestro, Vitor; Martini, Horst; Shonoda, Emad 13 2019 A hierarchical classification of Euclidean polytopes with regularity properties. Zbl 0812.51015 Martini, Horst 12 1994 Maximal sections and centrally symmetric bodies. Zbl 1012.52008 Makai, E. jun.; Martini, H.; Ódor, T. 12 2000 A new construction of Radon curves and related topics. Zbl 1372.52004 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 12 2016 Some results and problems around zonotopes. Zbl 0634.52007 Martini, H. 11 1987 Median and center hyperplanes in Minkowski spaces – a unified approach. Zbl 1010.51002 Martini, H.; Schöbel, A. 11 2001 The Fermat-Torricelli point and isosceles tetrahedra. Zbl 0795.51006 Kupitz, Yaakov S.; Martini, Horst 11 1994 Classical curve theory in normed planes. Zbl 1364.52005 Martini, Horst; Wu, Senlin 11 2014 Geometric properties of a sine function extendable to arbitrary normed planes. Zbl 1367.52005 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 11 2017 Cross-sectional measures. Zbl 0820.52003 Martini, H. 10 1994 New extensions of Napoleon’s theorem to higher dimensions. Zbl 1142.51015 Hajja, Mowaffaq; Martini, Horst; Spirova, Margarita 10 2008 Geometric constants for quantifying the difference between orthogonality types. Zbl 1365.46012 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 10 2016 Recent results in elementary geometry. II. Zbl 0852.51013 Martini, Horst 9 1995 Napoleon’s theorem with weights in \(n\)-space. Zbl 0920.51008 Martini, H.; Weißbach, B. 9 1999 Non-planar simplices are not reduced. Zbl 1048.52002 Martini, H.; Swanepoel, K. J. 9 2004 Minsum location extended to gauges and to convex sets. Zbl 1329.52010 Jahn, Thomas; Kupitz, Yaakov S.; Martini, Horst; Richter, Christian 9 2015 Surface immersions in normed spaces from the affine point of view. Zbl 1427.53010 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 9 2019 On Zindler curves in normed planes. Zbl 1276.52007 Martini, Horst; Wu, Senlin 9 2012 Ball convex bodies in Minkowski spaces. Zbl 1378.46015 Jahn, Thomas; Martini, Horst; Richter, Christian 9 2017 The Fermat-Torricelli problem. I: A discrete gradient-method approach. Zbl 1292.90282 Kupitz, Yaakov S.; Martini, Horst; Spirova, Margarita 9 2013 On the number of antipodal or strictly antipodal pairs of points in finite subsets of \(\mathbb{R}{}^ d\). Zbl 0738.52005 Makai, E. jun.; Martini, H. 8 1991 Equiframed curves – a generalization of Radon curves. Zbl 1071.52002 Martini, Horst; Swanepoel, Konrad J. 8 2004 Geometric algebra of strictly convex Minkowski planes. Zbl 1320.46015 Martini, Horst; Spirova, Margarita; Strambach, Karl 8 2014 Illumination and visibility problems in terms of closure operators. Zbl 1074.52001 Martini, Horst; Wenzel, Walter 8 2004 On reduced polytopes and antipodality. Zbl 1158.52012 Averkov, Gennadiy; Martini, Horst 8 2008 On maps preserving isosceles orthogonality in normed linear spaces. Zbl 1216.46008 Martini, Horst; Wu, Senlin 8 2009 Some applications of cross-section measures in Minkowski spaces. Zbl 1121.52022 Martini, H.; Mustafaev, Z. 8 2006 A new construction of curves of constant width. Zbl 1172.51309 Martini, Horst; Mustafaev, Zokhrab 8 2008 Orthocentric simplices and biregularity. Zbl 1146.51016 Edmonds, Allan L.; Hajja, Mowaffaq; Martini, Horst 8 2008 Radial projections of bisectors in Minkowski spaces. Zbl 1158.52007 Martini, Horst; Wu, Senlin 8 2008 Clifford’s chain of theorems in strictly convex Minkowski planes. Zbl 1174.51005 Martini, Horst; Spirova, Margarita 8 2008 On converses of Napoleon’s theorem and a modified shape function. Zbl 1116.51013 Hajja, Mowaffaq; Martini, Horst; Spirova, Margarita 8 2006 Reflections in strictly convex Minkowski planes. Zbl 1214.52002 Martini, Horst; Spirova, Margarita 7 2009 Approximating finite weighted point sets by hyperplanes. Zbl 0703.68097 Korneenko, N. M.; Martini, H. 7 1990 Combinatorial geometry of belt bodies. Zbl 0853.52004 Boltyanski, V.; Martini, H. 7 1995 On the isoperimetric inequalities for Reuleaux polygons. Zbl 0956.51011 Kupitz, Yaakov S.; Martini, Horst 7 2000 Generalized convexity notions and combinatorial geometry. Zbl 1051.52004 Martini, H.; Swanepoel, K. J. 7 2003 On bisectors for convex distance functions. Zbl 1302.46012 He, Chan; Martini, Horst; Wu, Senlin 7 2013 Complete sets need not be reduced in Minkowski spaces. Zbl 1347.52008 Martini, Horst; Wu, Senlin 7 2015 Illuminating and covering convex bodies. Zbl 1303.52009 Martini, Horst; Richter, Christian; Spirova, Margarita 7 2014 Two characterizations of smooth norms. Zbl 0952.52006 Martini, H.; Schöbel, A. 7 1999 Conics in normed planes. Zbl 1266.46011 Horváth, Ákos G.; Martini, Horst 7 2011 Chebyshev sets and ball operators. Zbl 1303.41014 Martín, Pedro; Martini, Horst; Spirova, Margarita 7 2014 Orthocentric simplices as the true generalizations of triangles. Zbl 1287.51011 Hajja, Mowaffaq; Martini, Horst 7 2013 On covering functionals of convex bodies. Zbl 1334.52007 He, Chan; Martini, Horst; Wu, Senlin 7 2016 Is a complete, reduced set necessarily of constant width? Zbl 1428.52004 Brandenberg, René; González Merino, Bernardo; Jahn, Thomas; Martini, Horst 7 2019 Shadow-boundaries of convex bodies. Zbl 0863.52003 Martini, Horst 6 1996 On the circular hull property in normed planes. Zbl 1212.46032 Martini, H.; Spirova, M. 6 2009 Convex polytopes whose projection bodies and difference sets are polars. Zbl 0679.52002 Martini, Horst 6 1991 Star-shaped sets in normed spaces. Zbl 0847.52003 Boltyanski, V.; Martini, H.; Soltan, P. S. 6 1996 Polygons derived from polygons via iterated constructions. Zbl 1341.51016 Donisi, Serena; Martini, Horst; Vincenzi, Giovanni; Vitale, Gaetano 6 2016 On the number of maximal regular simplices determined by \(n\) points in \(\mathbb R^d\). Zbl 1081.52016 Schur, Zvi; Perles, Micha A.; Martini, Horst; Kupitz, Yaakov S. 6 2003 Starshapedness vs. convexity. Zbl 1218.52004 Hansen, Guillermo; Martini, Horst 6 2011 Involutes of polygons of constant width in Minkowski planes. Zbl 1354.52003 Craizer, Marcos; Martini, Horst 6 2016 Angle measures, general rotations, and roulettes in normed planes. Zbl 1388.46016 Balestro, Vitor; Horváth, Ákos G.; Martini, Horst 6 2017 On the rotation index of bar billiards and Poncelet’s porism. Zbl 1278.53006 Cieślak, W.; Martini, H.; Mozgawa, W. 6 2013 Intersections of balls and sets of constant width in finite-dimensional normed spaces. Zbl 1278.52002 Martini, Horst; Richter, Christian; Spirova, Margarita 6 2013 Bi- and multifocal curves and surfaces for gauges. Zbl 1348.51006 Jahn, Thomas; Martini, Horst; Richter, Christian 6 2016 More characterizations of certain special families of simplices. Zbl 1335.52024 Hajja, M.; Hayajneh, M.; Martini, H. 6 2016 Low-degree minimal spanning trees in normed spaces. Zbl 1105.46010 Martini, Horst; Swanepoel, Konrad J. 6 2006 Jung’s theorem for a pair of Minkowski spaces. Zbl 1151.52006 Boltyanski, Vladimir; Martini, Horst 6 2006 Finite sets in \(\mathbb R^d\) with many diameters – a survey. Zbl 1141.51300 Kupitz, Y. S.; Martini, H.; Perles, M. A. 6 2005 Symmetrization of closure operators and visibility. Zbl 1099.06003 Martini, Horst; Wenzel, Walter 6 2005 Zur besten Beleuchtung konvexer Polyeder. Zbl 0543.52014 Martini, Horst; Weißbach, Bernulf 5 1984 Cassini curves in light field theory. (Cassini-Kurven in der Lichtfeldtheorie.) Zbl 0762.51011 Martini, Horst; Schiel, Uwe 5 1992 More recent results of elementary geometry. (Neuere Ergebnisse der Elementargeometrie.) Zbl 0815.51002 Martini, Horst 5 1994 A linear-time construction of Reuleaux polygons. Zbl 0876.52002 Kupitz, Yaakov; Martini, Horst; Wegner, Bernd 5 1996 An analogue of the Krein-Milman theorem for star-shaped sets. Zbl 1043.52006 Martini, Horst; Wenzel, Walter 5 2003 A characterization of convex sets via visibility. Zbl 1013.52005 Martini, H.; Wenzel, W. 5 2002 Differential geometry of immersed surfaces in three-dimensional normed spaces. Zbl 1475.53022 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 5 2020 Geometric dilation of closed curves in normed planes. Zbl 1161.65014 Martini, Horst; Wu, Senlin 5 2009 On Legendre curves in normed planes. Zbl 1408.46017 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 5 2018 A branch-and-bound approach for estimating covering functionals of convex bodies. Zbl 1518.52009 He, Chan; Lv, Yafang; Martini, Horst; Wu, Senlin 1 2023 Orthogonality types in normed linear spaces. Zbl 1503.46009 Alonso, Javier; Martini, Horst; Wu, Senlin 19 2022 The median triangle theorem as an entrance to certain issues in higher-dimensional geometry. Zbl 1502.51006 Hajja, Mowaffaq; Krasopoulos, Panagiotis T.; Martini, Horst 2 2022 Minkowski geometry – some concepts and recent developments. Zbl 1506.52001 Balestro, Vitor; Martini, Horst 1 2022 Some topics in differential geometry of normed spaces. Zbl 1510.53013 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 4 2021 Convex analysis in normed spaces and metric projections onto convex bodies. Zbl 1490.52007 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 4 2021 Duality of gauges and symplectic forms in vector spaces. Zbl 1482.52010 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 3 2021 Extremal problems for convex curves with a given self Chebyshev radius. Zbl 1469.52002 Balestro, Vitor; Martini, Horst; Nikonorov, Yurii; Nikonorova, Yulia 1 2021 Starshaped sets. Zbl 1454.52001 Hansen, G.; Herburt, I.; Martini, H.; Moszyńska, M. 13 2020 Differential geometry of immersed surfaces in three-dimensional normed spaces. Zbl 1475.53022 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 5 2020 On curvature of surfaces immersed in normed spaces. Zbl 1452.53005 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 4 2020 On Holditch’s theorem. Zbl 1440.53002 Cieślak, Waldemar; Martini, Horst; Mozgawa, Witold 3 2020 Tangent spheres of tetrahedra and a theorem of Grace. Zbl 1454.51009 Maehara, Hiroshi; Martini, Horst 2 2020 Curvature types of planar curves for gauges. Zbl 1452.46013 Balestro, Vitor; Martini, Horst; Sakaki, Makoto 2 2020 Differential geometry of spatial curves for gauges. Zbl 1467.46014 Balestro, Vitor; Martini, Horst; Sakaki, Makoto 1 2020 Concurrence of tetrahedral cevians associated with triangle centers. Zbl 1442.52008 Hajja, M.; Hammoudeh, I.; Hayajneh, M.; Martini, H. 1 2020 Crossing matchings and circuits have maximal length. Zbl 1495.05151 Kupitz, Yaakov S.; Last, Hagit; Martini, Horst; Perles, Micha A.; Pinchasi, Rom 1 2020 Bodies of constant width. An introduction to convex geometry with applications. Zbl 1468.52001 Martini, Horst; Montejano, Luis; Oliveros, Déborah 68 2019 Concepts of curvatures in normed planes. Zbl 1432.52001 Balestro, Vitor; Martini, Horst; Shonoda, Emad 13 2019 Surface immersions in normed spaces from the affine point of view. Zbl 1427.53010 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 9 2019 Is a complete, reduced set necessarily of constant width? Zbl 1428.52004 Brandenberg, René; González Merino, Bernardo; Jahn, Thomas; Martini, Horst 7 2019 The Rosenthal-Szasz inequality for normed planes. Zbl 1406.52004 Balestro, Vitor; Martini, Horst 4 2019 Optimal constants in normed planes. Zbl 1420.46015 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 3 2019 Bipartite sets of spheres and Casey-type theorems. Zbl 1409.51016 Maehara, Hiroshi; Martini, Horst 2 2019 On self-circumferences in Minkowski planes. Zbl 1427.52007 Ghandehari, Mostafa; Martini, Horst 1 2019 The inverse problem on roulettes in normed planes. Zbl 1452.46012 Balestro, Vitor; Horváth, Ákos G.; Martini, Horst 1 2019 On Legendre curves in normed planes. Zbl 1408.46017 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 5 2018 An analogue of Sylvester’s four-point problem on the sphere. Zbl 1449.60013 Maehara, H.; Martini, H. 4 2018 On the Erdős-Mordell inequality for normed planes and spaces. Zbl 1413.46018 Ghandehari, Mostafa; Martini, Horst 3 2018 Monge points, Euler lines, and Feuerbach spheres in Minkowski spaces. Zbl 1415.51030 Leopold, Undine; Martini, Horst 3 2018 A synthetic way to geometrize the method of coordinates. Zbl 1404.51015 Anatriello, Giuseppina; Martini, Horst; Vincenzi, Giovanni 1 2018 Touching perfect matchings and halving lines. Zbl 1411.05189 Perles, Micha A.; Martini, Horst; Kupitz, Yaakov S. 1 2018 Geometry of simplices in Minkowski spaces. Zbl 1400.51017 Leopold, Undine; Martini, Horst 1 2018 Uniqueness of completions and related topics. Zbl 1417.46012 He, Chan; Martini, Horst; Wu, Senlin 1 2018 Angles in normed spaces. Zbl 1365.52006 Balestro, Vitor; Horváth, Ákos G.; Martini, Horst; Teixeira, Ralph 22 2017 Geometric properties of a sine function extendable to arbitrary normed planes. Zbl 1367.52005 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 11 2017 Ball convex bodies in Minkowski spaces. Zbl 1378.46015 Jahn, Thomas; Martini, Horst; Richter, Christian 9 2017 Angle measures, general rotations, and roulettes in normed planes. Zbl 1388.46016 Balestro, Vitor; Horváth, Ákos G.; Martini, Horst 6 2017 On Lexell’s theorem. Zbl 1391.51017 Maehara, Hiroshi; Martini, Horst 4 2017 New moduli for Banach spaces. Zbl 1379.46018 Ivanov, G.; Martini, H. 4 2017 Geometric probability on the sphere. Zbl 1401.60019 Maehara, Hiroshi; Martini, Horst 3 2017 New inequalities for products of cross-section measures. Zbl 1377.52006 Martini, Horst; Mustafaev, Zokhrab 3 2017 Outer normal transforms of convex polytopes. Zbl 1378.52012 Maehara, Hiroshi; Martini, Horst 2 2017 Holding convex polyhedra by circular rings. Zbl 1406.52006 Maehara, Hiroshi; Martini, Horst 1 2017 Locally 3-transitive graphs of girth 4. Zbl 1359.05032 Perles, Micha A.; Martini, Horst; Kupitz, Yaakov S. 1 2017 A new construction of Radon curves and related topics. Zbl 1372.52004 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 12 2016 Geometric constants for quantifying the difference between orthogonality types. Zbl 1365.46012 Balestro, Vitor; Martini, Horst; Teixeira, Ralph 10 2016 On covering functionals of convex bodies. Zbl 1334.52007 He, Chan; Martini, Horst; Wu, Senlin 7 2016 Polygons derived from polygons via iterated constructions. Zbl 1341.51016 Donisi, Serena; Martini, Horst; Vincenzi, Giovanni; Vitale, Gaetano 6 2016 Involutes of polygons of constant width in Minkowski planes. Zbl 1354.52003 Craizer, Marcos; Martini, Horst 6 2016 Bi- and multifocal curves and surfaces for gauges. Zbl 1348.51006 Jahn, Thomas; Martini, Horst; Richter, Christian 6 2016 More characterizations of certain special families of simplices. Zbl 1335.52024 Hajja, M.; Hayajneh, M.; Martini, H. 6 2016 Minsum location extended to gauges and to convex sets. Zbl 1329.52010 Jahn, Thomas; Kupitz, Yaakov S.; Martini, Horst; Richter, Christian 9 2015 Complete sets need not be reduced in Minkowski spaces. Zbl 1347.52008 Martini, Horst; Wu, Senlin 7 2015 Orthogonalities, transitivity of norms and characterizations of Hilbert spaces. Zbl 1322.46009 Martini, Horst; Wu, Senlin 5 2015 Algorithms for ball hulls and ball intersections in normed planes. Zbl 1408.52025 Martín, Pedro; Martini, Horst 2 2015 Centered convex bodies and inequalities for cross-section measures. Zbl 1331.52007 Martini, Horst; Mustafaev, Zokhrab 1 2015 Reduced convex bodies in finite dimensional normed spaces: a survey. Zbl 1310.52004 Lassak, Marek; Martini, Horst 14 2014 Classical curve theory in normed planes. Zbl 1364.52005 Martini, Horst; Wu, Senlin 11 2014 Geometric algebra of strictly convex Minkowski planes. Zbl 1320.46015 Martini, Horst; Spirova, Margarita; Strambach, Karl 8 2014 Illuminating and covering convex bodies. Zbl 1303.52009 Martini, Horst; Richter, Christian; Spirova, Margarita 7 2014 Chebyshev sets and ball operators. Zbl 1303.41014 Martín, Pedro; Martini, Horst; Spirova, Margarita 7 2014 On translative coverings of convex bodies. Zbl 1305.52022 Lassak, Marek; Martini, Horst; Spirova, Margarita 3 2014 Complete sets and completion of sets in Banach spaces. Zbl 1311.46015 Martini, Horst; Papini, Pier Luigi; Spirova, Margarita 3 2014 Characterizations of \(l_\infty^n\) and \(l_1^n\), and their stabilities. Zbl 1294.52006 Martini, Horst; Wu, Senlin 2 2014 Rotation indices related to Poncelet’s closure theorem. Zbl 1312.51005 Cieślak, Waldemar; Martini, Horst; Mozgawa, Witold 1 2014 Dispensable points, radial functions, and boundaries of starshaped sets. Zbl 1340.52002 Hansen, Guillermo; Martini, Horst 1 2014 On a theorem of D. Ryabogin and V. Yaskin about detecting symmetry. Zbl 1381.52011 Makai, E. jun.; Martini, H.; Ódor, T. 1 2014 The Fermat-Torricelli problem. I: A discrete gradient-method approach. Zbl 1292.90282 Kupitz, Yaakov S.; Martini, Horst; Spirova, Margarita 9 2013 On bisectors for convex distance functions. Zbl 1302.46012 He, Chan; Martini, Horst; Wu, Senlin 7 2013 Orthocentric simplices as the true generalizations of triangles. Zbl 1287.51011 Hajja, Mowaffaq; Martini, Horst 7 2013 On the rotation index of bar billiards and Poncelet’s porism. Zbl 1278.53006 Cieślak, W.; Martini, H.; Mozgawa, W. 6 2013 Intersections of balls and sets of constant width in finite-dimensional normed spaces. Zbl 1278.52002 Martini, Horst; Richter, Christian; Spirova, Margarita 6 2013 Bounded representation and radial projections of bisectors in normed spaces. Zbl 1273.46005 Horváth, Á. G.; Martini, H. 4 2013 Cassini curves in normed planes. Zbl 1276.52008 Martini, Horst; Wu, Senlin 3 2013 On reduced triangles in normed planes. Zbl 1296.46011 Alonso, Javier; Martini, Horst; Spirova, Margarita 3 2013 Proposition 21 of Book I of Euclid’s Elements: variants, generalizations, and open questions. Zbl 1303.51010 Hajja, Mowaffaq; Martini, Horst 2 2013 Locally symmetric graphs of girth 4. Zbl 1264.05087 Perles, Micha A.; Martini, Horst; Kupitz, Yaakov S. 2 2013 Concurrency of the altitudes of a triangle. Zbl 1291.51012 Hajja, Mowaffaq; Martini, Horst 2 2013 On the polygonal diameter (= link diameter) of the interior, resp. exterior, of a simple closed polygon in the plane. Zbl 1294.52003 Perles, Micha A.; Martini, Horst; Kupitz, Yaakov S. 1 2013 On universal covers in normed planes. Zbl 1266.52010 Martini, Horst; Spirova, Margarita 1 2013 Discrete geometry in Minkowski spaces. Zbl 1290.52007 Alonso, Javier; Martini, Horst; Spirova, Margarita 1 2013 On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces. Zbl 1241.46006 Alonso, Javier; Martini, Horst; Wu, Senlin 122 2012 Minimal enclosing discs, circumcircles, and circumcenters in normed planes. I. Zbl 1245.65022 Alonso, Javier; Martini, Horst; Spirova, Margarita 15 2012 Minimal enclosing discs, circumcircles, and circumcenters in normed planes. II. Zbl 1251.65016 Alonso, Javier; Martini, Horst; Spirova, Margarita 14 2012 On Zindler curves in normed planes. Zbl 1276.52007 Martini, Horst; Wu, Senlin 9 2012 Minsum hyperspheres in normed spaces. Zbl 1250.90049 Körner, Mark-Christoph; Martini, Horst; Schöbel, Anita 4 2012 On unit balls and isoperimetrices in normed spaces. Zbl 1259.46009 Martini, Horst; Mustafaev, Zokhrab 3 2012 Centrally symmetric convex bodies and sections having maximal quermassintegrals. Zbl 1265.52005 Makai, E. jun.; Martini, H. 3 2012 On the self-perimeter of pentagonal gauges. Zbl 1260.46011 Martini, Horst; Shcherba, Anatoly 1 2012 Reduced convex bodies in Euclidean space – a survey. Zbl 1213.52006 Lassak, Marek; Martini, Horst 20 2011 Conics in normed planes. Zbl 1266.46011 Horváth, Ákos G.; Martini, Horst 7 2011 Starshapedness vs. convexity. Zbl 1218.52004 Hansen, Guillermo; Martini, Horst 6 2011 On orthogonal chords in normed planes. Zbl 1214.52001 Alonso, Javier; Martini, Horst; Mustafaev, Zokhrab 5 2011 An integral formula related to inner isoptics. Zbl 1252.52003 Martini, Horst; Mozgawa, Witold 4 2011 Geometry where direction matters – or does it? Zbl 1233.52005 Martini, Horst; Spirova, Margarita; Swanepoel, Konrad J. 2 2011 On the self-perimeter of quadrangles for gauges. Zbl 1222.52001 Martini, H.; Shcherba, A. 2 2011 Ball polytopes and the Vázsonyi problem. Zbl 1224.52025 Kupitz, Y. S.; Martini, H.; Perles, M. A. 19 2010 On isoperimetric inequalities in Minkowski spaces. Zbl 1196.52007 Martini, Horst; Mustafaev, Zokhrab 4 2010 On closed starshaped sets. Zbl 1207.52006 Hansen, Guillermo; Martini, Horst 4 2010 ...and 133 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 884 Authors 121 Martini, Horst 30 Wu, Senlin 25 Balestro, Vitor 20 Hajja, Mowaffaq 20 Spirova, Margarita Georgieva 18 Swanepoel, Konrad J. 17 Tanaka, Ryotaro 15 He, Chan 15 Teixeira, Ralph Costa 14 Lassak, Marek 14 Raĭgorodskiĭ, Andreĭ Mikhaĭlovich 14 Zachos, Anastasios N. 12 Schöbel, Anita 11 Horváth, Ákos G. 11 Kupitz, Yaakov S. 11 Li, Yongjin 11 Sain, Debmalya 10 Bezdek, Károly 10 Cheng, Ray 10 Lángi, Zsolt 10 Mozgawa, Witold 10 Rochera, David 10 Soltan, Valeriu 9 Alonso, Javier 9 Brandenberg, René 9 González Merino, Bernardo 9 Jahn, Thomas 8 Hayajneh, Mostafa 8 Maehara, Hiroshi 8 Moreno, José-Pedro 8 Nam, Nguyen Mau 8 Saito, Kichisuke 8 Schulte, Egon 7 Fodor, Ferenc 7 Kurusa, Árpád 7 Montejano Peimbert, Luis 7 Mustafaev, Zokhrab 7 Naszódi, Márton 7 Papini, Pier Luigi 7 Richter, Christian 7 Wójcik, Paweł 6 Arambašić, Ljiljana 6 Berele, Allan 6 Boltyanskij, Vladimir Grigor’evich 6 Catoiu, Stefan 6 Jin, Hailin 6 Komuro, Naoto 6 Nikonorov, Yurii Gennadyevich 6 Perles, Micha A. 6 Plastria, Frank 6 Schneider, Rolf G. 6 Vincenzi, Giovanni 6 Zamani, Ali 6 Zong, Chuanming 5 Bracho, Javier 5 Chmieliński, Jacek 5 Cieślak, Waldemar 5 Craizer, Marcos 5 Kupavskii, Andrey 5 Moslehian, Mohammad Sal 5 Paul, Kallol 5 Polyanskiĭ, Aleksandr Andreevich 5 Ross, William T. 5 Xi, Lifeng 4 Alimov, Alexey R. 4 Bisztriczky, Tibor 4 Bottazzi, Tamara 4 Brazil, Marcus N. 4 Breen, Marilyn 4 Cabello Sánchez, Javier 4 Di Stefano, Gabriele 4 Gunawan, Hendra 4 Guterman, Alexander Èmilevich 4 Hammoudeh, Ismail 4 Hug, Daniel 4 Laudano, Francesco 4 Leng, Gangsong 4 Mizuguchi, Hiroyasu 4 Monson, Barry 4 Navarra, Alfredo 4 Oliveros, Deborah 4 Pach, János 4 Pushnyakov, Filipp Anatol’evich 4 Pyaderkin, M. M. 4 Rajić, Rajna 4 Ras, Charl J. 4 Saleh, Wedad 4 Skrzypiec, Magdalena 4 Tabachnikov, Serge L. 4 Thomas, Doreen Anne 4 Väisälä, Jussi 4 Vígh, Viktor 4 Weiß, Gunter 4 Wenzel, Walter 3 An, Nguyen Thai 3 Arocha, Jorge Luis 3 Averkov, Gennadiy 3 Azhmyakov, Vadim 3 Baronti, Marco 3 Berestovskiĭ, Valeriĭ Nikolaevich ...and 784 more Authors all top 5 Cited in 231 Serials 84 Beiträge zur Algebra und Geometrie 47 Aequationes Mathematicae 40 Journal of Mathematical Analysis and Applications 34 Discrete & Computational Geometry 32 Journal of Geometry 25 Results in Mathematics 22 Journal of Optimization Theory and Applications 17 Mathematical Notes 16 Linear Algebra and its Applications 14 Mathematika 13 Journal of Convex Analysis 12 Discrete Mathematics 12 Advances in Mathematics 11 Periodica Mathematica Hungarica 11 Monatshefte für Mathematik 10 Archiv der Mathematik 10 Computational Geometry 10 Mathematical Inequalities & Applications 10 Advances in Geometry 9 Israel Journal of Mathematics 9 Transactions of the American Mathematical Society 8 Geometriae Dedicata 8 Expositiones Mathematicae 8 Journal of Mathematical Sciences (New York) 8 Mediterranean Journal of Mathematics 7 Proceedings of the American Mathematical Society 7 European Journal of Operational Research 7 Annals of Functional Analysis 6 Discrete Applied Mathematics 6 Acta Mathematica Hungarica 6 Fractals 6 Doklady Mathematics 5 Bulletin of the Australian Mathematical Society 5 Linear and Multilinear Algebra 5 The Mathematical Intelligencer 5 Computer Aided Geometric Design 5 The Journal of Geometric Analysis 5 Journal of Inequalities and Applications 4 American Mathematical Monthly 4 Mathematische Semesterberichte 4 Problems of Information Transmission 4 Rocky Mountain Journal of Mathematics 4 Journal of Geometry and Physics 4 Journal of Combinatorial Theory. Series A 4 Pacific Journal of Mathematics 4 Topology and its Applications 4 European Journal of Combinatorics 4 Elemente der Mathematik 4 Journal for Geometry and Graphics 4 Discrete Optimization 4 Journal of Function Spaces 3 Inverse Problems 3 Studia Mathematica 3 Canadian Mathematical Bulletin 3 Journal of Functional Analysis 3 Acta Applicandae Mathematicae 3 Journal of Global Optimization 3 Calculus of Variations and Partial Differential Equations 3 Journal of Combinatorial Optimization 3 Acta Mathematica Sinica. English Series 3 Journal of Mathematical Inequalities 3 Banach Journal of Mathematical Analysis 3 Ars Mathematica Contemporanea 3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 3 The Art of Discrete and Applied Mathematics 2 Archive for History of Exact Sciences 2 Computer Methods in Applied Mechanics and Engineering 2 International Journal of Mathematical Education in Science and Technology 2 Information Processing Letters 2 Journal of the Franklin Institute 2 Nonlinearity 2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Applied Mathematics and Computation 2 Journal of Applied Probability 2 Journal of Approximation Theory 2 Journal of Graph Theory 2 Kyungpook Mathematical Journal 2 Mathematische Nachrichten 2 Networks 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Rendiconti del Seminario Matematico della Università di Padova 2 Theoretical Computer Science 2 Advances in Applied Mathematics 2 Optimization 2 Computers & Operations Research 2 Applied Mathematics Letters 2 SIAM Journal on Discrete Mathematics 2 Science in China. Series A 2 Differential Geometry and its Applications 2 Distributed Computing 2 Mathematical Programming. Series A. Series B 2 Journal of Algebraic Combinatorics 2 Top 2 Optimization Methods & Software 2 Communications in Contemporary Mathematics 2 Bulletin of the Brazilian Mathematical Society. New Series 2 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 2 4OR ...and 131 more Serials all top 5 Cited in 49 Fields 485 Convex and discrete geometry (52-XX) 222 Functional analysis (46-XX) 209 Geometry (51-XX) 83 Differential geometry (53-XX) 73 Combinatorics (05-XX) 73 Operations research, mathematical programming (90-XX) 42 Operator theory (47-XX) 32 Computer science (68-XX) 28 Calculus of variations and optimal control; optimization (49-XX) 27 Numerical analysis (65-XX) 21 Real functions (26-XX) 20 Probability theory and stochastic processes (60-XX) 18 Linear and multilinear algebra; matrix theory (15-XX) 17 Algebraic geometry (14-XX) 16 General topology (54-XX) 13 Functions of a complex variable (30-XX) 11 Measure and integration (28-XX) 11 Dynamical systems and ergodic theory (37-XX) 11 Difference and functional equations (39-XX) 11 Approximations and expansions (41-XX) 11 Statistics (62-XX) 9 Global analysis, analysis on manifolds (58-XX) 8 Group theory and generalizations (20-XX) 8 Systems theory; control (93-XX) 7 History and biography (01-XX) 7 Partial differential equations (35-XX) 7 Mathematics education (97-XX) 6 Number theory (11-XX) 6 Manifolds and cell complexes (57-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 General and overarching topics; collections (00-XX) 4 Ordinary differential equations (34-XX) 4 Mechanics of deformable solids (74-XX) 4 Information and communication theory, circuits (94-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Integral transforms, operational calculus (44-XX) 3 Algebraic topology (55-XX) 3 Mechanics of particles and systems (70-XX) 3 Geophysics (86-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Field theory and polynomials (12-XX) 2 Topological groups, Lie groups (22-XX) 2 Potential theory (31-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Special functions (33-XX) 2 Fluid mechanics (76-XX) 2 Biology and other natural sciences (92-XX) 1 Commutative algebra (13-XX) 1 Statistical mechanics, structure of matter (82-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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