Edit Profile (opens in new tab) Martini, Horst Compute Distance To: Compute Author ID: martini.horst Published as: Martini, Horst; Martini, H. Homepage: https://www.tu-chemnitz.de/mathematik/geometrie/index.php External Links: MGP · dblp · GND Documents Indexed: 286 Publications since 1984, including 4 Books 2 Contributions as Editor Reviewing Activity: 483 Reviews Biographic References: 1 Publication Co-Authors: 70 Co-Authors with 253 Joint Publications 904 Co-Co-Authors all top 5 Co-Authors 33 single-authored 30 Spirova, Margarita Georgieva 28 Kupitz, Yaakov S. 24 Wu, Senlin 22 Balestro, Vitor 16 Makai, Endre jun. 14 Boltyanskij, Vladimir Grigor’evich 14 Maehara, Hiroshi 14 Teixeira, Ralph Costa 12 Hajja, Mowaffaq 12 Mustafaev, Zokhrab 12 Swanepoel, Konrad J. 11 Perles, Micha A. 11 Soltan, Valeriu 8 Alonso, Javier 8 Wenzel, Walter 6 Averkov, Gennadiy 6 Soltan, Petru 5 Horváth, Ákos G. 5 Richter, Christian 5 Schöbel, Anita 4 He, Chan 4 Jahn, Thomas 4 Lassak, Marek 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 Martín Jimenez, Pedro 3 Ódor, Tibor 2 Hayajneh, Mostafa 2 Korneenko, Nikolai M. 2 Leopold, Undine 2 Sakaki, Makoto 2 Vincenzi, Giovanni 2 Wegner, Bernd 1 Anatriello, Giuseppina 1 Bordei, Alexei 1 Brandenberg, René 1 Craizer, Marcos 1 de Wet, Pieter Oloff 1 Donisi, Serena 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 Merino, Bernardo González 1 Montejano Peimbert, Luis 1 Moszyńska, Maria 1 Nam, Nguyen Mau 1 Nguyên Manh Hung 1 Nikonorov, Yurii Gennadyevich 1 Nikonorova, Yulia V. 1 Oliveros, Deborah 1 Papini, Pier Luigi 1 Pinchasi, Rom 1 Prisacaru, Kiril 1 Robinson, Adam 1 Schiel, Uwe 1 Schur, Zvi 1 Shonoda, Emad N. 1 Strambach, Karl 1 Vitale, Gaetano all top 5 Serials 23 Beiträge zur Algebra und Geometrie 14 Results in Mathematics 13 Aequationes Mathematicae 9 Periodica Mathematica Hungarica 9 Geometriae Dedicata 8 Journal of Geometry 8 Studia Scientiarum Mathematicarum Hungarica 8 Journal of Convex Analysis 7 Discrete Mathematics 6 Colloquium Mathematicum 6 Acta Mathematica Hungarica 5 Monatshefte für Mathematik 5 Discrete & Computational Geometry 5 Extracta Mathematicae 5 Advances in Geometry 4 Rocky Mountain Journal of Mathematics 4 Acta Scientiarum Mathematicarum 4 Archiv der Mathematik 4 Canadian Mathematical Bulletin 4 Journal of Optimization Theory and Applications 4 Elemente der Mathematik 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 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 Annals of Functional Analysis 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 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 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 São Paulo Journal of Mathematical Sciences 1 Journal of Computational Geometry 1 Southeast Asian Journal of Sciences 1 Universitext all top 5 Fields 225 Convex and discrete geometry (52-XX) 92 Geometry (51-XX) 82 Functional analysis (46-XX) 27 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 Numerical analysis (65-XX) 4 General and overarching topics; collections (00-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 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 214 Publications have been cited 1,577 times in 719 Documents Cited by ▼ Year ▼ The geometry of Minkowski spaces – a survey. I. Zbl 0984.52004Martini, Horst; Swanepoel, Konrad J.; Weiß, Gunter 102 2001 On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces. Zbl 1241.46006Alonso, Javier; Martini, Horst; Wu, Senlin 102 2012 Excursions into combinatorial geometry. Zbl 0877.52001Boltyanski, V.; Martini, H.; Soltan, Petru S. 93 1997 The geometry of Minkowski spaces – a survey. II. Zbl 1080.52005Martini, H.; Swanepoel, K. J. 76 2004 Geometric methods and optimization problems. Zbl 0933.90002Boltyanski, V.; Martini, H.; Soltan, V. 52 1999 Antinorms and Radon curves. Zbl 1108.52005Martini, Horst; Swanepoel, Konrad J. 51 2006 Combinatorial problems on the illumination of convex bodies. Zbl 0937.52006Martini, Horst; Soltan, Valeriu 42 1999 Geometric aspects of the generalized Fermat-Torricelli problem. Zbl 0911.51021Kupitz, Y. S.; Martini, H. 37 1997 Special convex bodies. Zbl 0794.52002Heil, E.; Martini, H. 36 1993 Bodies of constant width. An introduction to convex geometry with applications. Zbl 1468.52001Martini, Horst; Montejano, Luis; Oliveros, Déborah 30 2019 The Fermat–Torricelli problem in normed planes and spaces. Zbl 1047.90032Martini, H.; Swanepoel, K. J.; Weiss, G. 28 2002 Angles in normed spaces. Zbl 1365.52006Balestro, Vitor; Horváth, Ákos G.; Martini, Horst; Teixeira, Ralph 18 2017 Orthocentric simplices and their centers. Zbl 1084.51008Edmonds, Allan L.; Hajja, Mowaffaq; Martini, Horst 16 2005 Antipodality properties of finite sets in Euclidean space. Zbl 1066.52010Martini, H.; Soltan, V. 15 2005 Ball polytopes and the Vázsonyi problem. Zbl 1224.52025Kupitz, Y. S.; Martini, H.; Perles, M. A. 15 2010 Hyperplane approximation and related topics. Zbl 0809.52013Korneenko, Nikolai M.; Martini, Horst 14 1993 Reduced convex bodies in Euclidean space – a survey. Zbl 1213.52006Lassak, Marek; Martini, Horst 14 2011 Minimal enclosing discs, circumcircles, and circumcenters in normed planes. I. Zbl 1245.65022Alonso, Javier; Martini, Horst; Spirova, Margarita 14 2012 The Feuerbach circle and orthocentricity in normed places. Zbl 1144.52001Martini, Horst; Spirova, Margarita 13 2007 On the theorem of Napoleon and related topics. Zbl 0864.51009Martini, Horst 13 1996 Coincidences of simplex centers and related facial structures. Zbl 1093.51014Edmonds, Allan L.; Hajja, Mowaffaq; Martini, Horst 13 2005 Minimal enclosing discs, circumcircles, and circumcenters in normed planes. II. Zbl 1251.65016Alonso, Javier; Martini, Horst; Spirova, Margarita 13 2012 Reduced bodies in Minkowski space. Zbl 1084.52004Lassak, M.; Martini, H. 12 2005 Geometric properties of a sine function extendable to arbitrary normed planes. Zbl 1367.52005Balestro, Vitor; Martini, Horst; Teixeira, Ralph 12 2017 Reduced convex bodies in finite dimensional normed spaces: a survey. Zbl 1310.52004Lassak, Marek; Martini, Horst 12 2014 The cross-section body, plane sections of convex bodies and approximation of convex bodies. I. Zbl 0865.52005Makai, E. jun.; Martini, H. 11 1996 Median hyperplanes in normed spaces – a survey. Zbl 0921.90109Martini, Horst; Schöbel, Anita 11 1998 Maximal sections and centrally symmetric bodies. Zbl 1012.52008Makai, E. jun.; Martini, H.; Ódor, T. 11 2000 The Fermat-Torricelli point and isosceles tetrahedra. Zbl 0795.51006Kupitz, Yaakov S.; Martini, Horst 10 1994 New extensions of Napoleon’s theorem to higher dimensions. Zbl 1142.51015Hajja, Mowaffaq; Martini, Horst; Spirova, Margarita 10 2008 Napoleon’s theorem with weights in \(n\)-space. Zbl 0920.51008Martini, H.; Weißbach, B. 10 1999 Median and center hyperplanes in Minkowski spaces – a unified approach. Zbl 1010.51002Martini, H.; Schöbel, A. 10 2001 Geometric constants for quantifying the difference between orthogonality types. Zbl 1365.46012Balestro, Vitor; Martini, Horst; Teixeira, Ralph 10 2016 Minsum location extended to gauges and to convex sets. Zbl 1329.52010Jahn, Thomas; Kupitz, Yaakov S.; Martini, Horst; Richter, Christian 9 2015 Classical curve theory in normed planes. Zbl 1364.52005Martini, Horst; Wu, Senlin 9 2014 A hierarchical classification of Euclidean polytopes with regularity properties. Zbl 0812.51015Martini, Horst 8 1994 Illumination and visibility problems in terms of closure operators. Zbl 1074.52001Martini, Horst; Wenzel, Walter 8 2004 Equiframed curves – a generalization of Radon curves. Zbl 1071.52002Martini, Horst; Swanepoel, Konrad J. 8 2004 On converses of Napoleon’s theorem and a modified shape function. Zbl 1116.51013Hajja, Mowaffaq; Martini, Horst; Spirova, Margarita 8 2006 Radial projections of bisectors in Minkowski spaces. Zbl 1158.52007Martini, Horst; Wu, Senlin 8 2008 On reduced polytopes and antipodality. Zbl 1158.52012Averkov, Gennadiy; Martini, Horst 8 2008 A new construction of Radon curves and related topics. Zbl 1372.52004Balestro, Vitor; Martini, Horst; Teixeira, Ralph 8 2016 On Zindler curves in normed planes. Zbl 1276.52007Martini, Horst; Wu, Senlin 8 2012 Surface immersions in normed spaces from the affine point of view. Zbl 1427.53010Balestro, Vitor; Martini, Horst; Teixeira, Ralph 8 2019 Cross-sectional measures. Zbl 0820.52003Martini, H. 7 1994 Non-planar simplices are not reduced. Zbl 1048.52002Martini, H.; Swanepoel, K. J. 7 2004 Geometric algebra of strictly convex Minkowski planes. Zbl 1320.46015Martini, Horst; Spirova, Margarita; Strambach, Karl 7 2014 Recent results in elementary geometry. II. Zbl 0852.51013Martini, Horst 7 1995 On maps preserving isosceles orthogonality in normed linear spaces. Zbl 1216.46008Martini, Horst; Wu, Senlin 7 2009 Some applications of cross-section measures in Minkowski spaces. Zbl 1121.52022Martini, H.; Mustafaev, Z. 7 2006 Approximating finite weighted point sets by hyperplanes. Zbl 0703.68097Korneenko, N. M.; Martini, H. 7 1990 On the number of antipodal or strictly antipodal pairs of points in finite subsets of \(\mathbb{R}{}^ d\). Zbl 0738.52005Makai, E. jun.; Martini, H. 7 1991 Concepts of curvatures in normed planes. Zbl 1432.52001Balestro, Vitor; Martini, Horst; Shonoda, Emad 7 2019 Orthocentric simplices and biregularity. Zbl 1146.51016Edmonds, Allan L.; Hajja, Mowaffaq; Martini, Horst 7 2008 Clifford’s chain of theorems in strictly convex Minkowski planes. Zbl 1174.51005Martini, Horst; Spirova, Margarita 7 2008 Involutes of polygons of constant width in Minkowski planes. Zbl 1354.52003Craizer, Marcos; Martini, Horst 7 2016 The Fermat-Torricelli problem. I: A discrete gradient-method approach. Zbl 1292.90282Kupitz, Yaakov S.; Martini, Horst; Spirova, Margarita 7 2013 Orthocentric simplices as the true generalizations of triangles. Zbl 1287.51011Hajja, Mowaffaq; Martini, Horst 7 2013 Starshaped sets. Zbl 1454.52001Hansen, G.; Herburt, I.; Martini, H.; Moszyńska, M. 7 2020 On the isoperimetric inequalities for Reuleaux polygons. Zbl 0956.51011Kupitz, Yaakov S.; Martini, Horst 6 2000 Generalized convexity notions and combinatorial geometry. Zbl 1051.52004Martini, H.; Swanepoel, K. J. 6 2003 Chebyshev sets and ball operators. Zbl 1303.41014Martín, Pedro; Martini, Horst; Spirova, Margarita 6 2014 Shadow-boundaries of convex bodies. Zbl 0863.52003Martini, Horst 6 1996 Starshapedness vs. convexity. Zbl 1218.52004Hansen, Guillermo; Martini, Horst 6 2011 Jung’s theorem for a pair of Minkowski spaces. Zbl 1151.52006Boltyanski, Vladimir; Martini, Horst 6 2006 On the number of maximal regular simplices determined by \(n\) points in \(\mathbb R^d\). Zbl 1081.52016Schur, Zvi; Perles, Micha A.; Martini, Horst; Kupitz, Yaakov S. 6 2003 Two characterizations of smooth norms. Zbl 0952.52006Martini, H.; Schöbel, A. 6 1999 Reflections in strictly convex Minkowski planes. Zbl 1214.52002Martini, Horst; Spirova, Margarita 6 2009 A new construction of curves of constant width. Zbl 1172.51309Martini, Horst; Mustafaev, Zokhrab 6 2008 Symmetrization of closure operators and visibility. Zbl 1099.06003Martini, Horst; Wenzel, Walter 6 2005 Low-degree minimal spanning trees in normed spaces. Zbl 1105.46010Martini, Horst; Swanepoel, Konrad J. 6 2006 Convex polytopes whose projection bodies and difference sets are polars. Zbl 0679.52002Martini, Horst 6 1991 On the rotation index of bar billiards and Poncelet’s porism. Zbl 1278.53006Cieślak, W.; Martini, H.; Mozgawa, W. 6 2013 Conics in normed planes. Zbl 1266.46011Horváth, Ákos G.; Martini, Horst 6 2011 Bi- and multifocal curves and surfaces for gauges. Zbl 1348.51006Jahn, Thomas; Martini, Horst; Richter, Christian 6 2016 Ball convex bodies in Minkowski spaces. Zbl 1378.46015Jahn, Thomas; Martini, Horst; Richter, Christian 6 2017 An analogue of the Krein-Milman theorem for star-shaped sets. Zbl 1043.52006Martini, Horst; Wenzel, Walter 5 2003 Illuminating and covering convex bodies. Zbl 1303.52009Martini, Horst; Richter, Christian; Spirova, Margarita 5 2014 Combinatorial geometry of belt bodies. Zbl 0853.52004Boltyanski, V.; Martini, H. 5 1995 Star-shaped sets in normed spaces. Zbl 0847.52003Boltyanski, V.; Martini, H.; Soltan, P. S. 5 1996 On orthogonal chords in normed planes. Zbl 1214.52001Alonso, Javier; Martini, Horst; Mustafaev, Zokhrab 5 2011 A linear-time construction of Reuleaux polygons. Zbl 0876.52002Kupitz, Yaakov; Martini, Horst; Wegner, Bernd 5 1996 On the circular hull property in normed planes. Zbl 1212.46032Martini, H.; Spirova, M. 5 2009 A characterization of convex sets via visibility. Zbl 1013.52005Martini, H.; Wenzel, W. 5 2002 On Reuleaux triangles in Minkowski planes. Zbl 1121.52006Martini, Horst; Mustafaev, Zokhrab 5 2007 Zur besten Beleuchtung konvexer Polyeder. Zbl 0543.52014Martini, Horst; Weißbach, Bernulf 5 1984 Geometric dilation of closed curves in normed planes. Zbl 1161.65014Martini, Horst; Wu, Senlin 5 2009 Finite sets in \(\mathbb R^d\) with many diameters – a survey. Zbl 1141.51300Kupitz, Y. S.; Martini, H.; Perles, M. A. 5 2005 Polygons derived from polygons via iterated constructions. Zbl 1341.51016Donisi, Serena; Martini, Horst; Vincenzi, Giovanni; Vitale, Gaetano 5 2016 Intersections of balls and sets of constant width in finite-dimensional normed spaces. Zbl 1278.52002Martini, Horst; Richter, Christian; Spirova, Margarita 5 2013 On orthocentric systems in strictly convex normed planes. Zbl 1196.52003Martini, Horst; Wu, Senlin 5 2009 An integral formula related to inner isoptics. Zbl 1252.52003Martini, Horst; Mozgawa, Witold 4 2011 Regular polytopes and generalizations. (Reguläre Polytope und Verallgemeinerungen.) Zbl 0810.52011Martini, Horst 4 1994 More characterizations of certain special families of simplices. Zbl 1335.52024Hajja, M.; Hayajneh, M.; Martini, H. 4 2016 On bisectors for convex distance functions. Zbl 1302.46012He, Chan; Martini, Horst; Wu, Senlin 4 2013 On covering functionals of convex bodies. Zbl 1334.52007He, Chan; Martini, Horst; Wu, Senlin 4 2016 Cassini curves in light field theory. (Cassini-Kurven in der Lichtfeldtheorie.) Zbl 0762.51011Martini, Horst; Schiel, Uwe 4 1992 On regular 4-coverings and their application for lattice coverings in normed planes. Zbl 1186.52007Martini, Horst; Spirova, Margarita 4 2009 On pyramids and reducedness. Zbl 1199.52008Averkov, Gennadiy; Martini, Horst 4 2008 Circle geometry in affine Cayley-Klein planes. Zbl 1199.51013Martini, Horst; Spirova, Margarita 4 2008 Some topics in differential geometry of normed spaces. Zbl 07335423Balestro, Vitor; Martini, Horst; Teixeira, Ralph 2 2021 Duality of gauges and symplectic forms in vector spaces. Zbl 1482.52010Balestro, Vitor; Martini, Horst; Teixeira, Ralph 2 2021 Starshaped sets. Zbl 1454.52001Hansen, G.; Herburt, I.; Martini, H.; Moszyńska, M. 7 2020 On curvature of surfaces immersed in normed spaces. Zbl 1452.53005Balestro, Vitor; Martini, Horst; Teixeira, Ralph 4 2020 Differential geometry of immersed surfaces in three-dimensional normed spaces. Zbl 1475.53022Balestro, Vitor; Martini, Horst; Teixeira, Ralph 2 2020 On Holditch’s theorem. Zbl 1440.53002Cieślak, Waldemar; Martini, Horst; Mozgawa, Witold 1 2020 Curvature types of planar curves for gauges. Zbl 1452.46013Balestro, Vitor; Martini, Horst; Sakaki, Makoto 1 2020 Bodies of constant width. An introduction to convex geometry with applications. Zbl 1468.52001Martini, Horst; Montejano, Luis; Oliveros, Déborah 30 2019 Surface immersions in normed spaces from the affine point of view. Zbl 1427.53010Balestro, Vitor; Martini, Horst; Teixeira, Ralph 8 2019 Concepts of curvatures in normed planes. Zbl 1432.52001Balestro, Vitor; Martini, Horst; Shonoda, Emad 7 2019 Is a complete, reduced set necessarily of constant width? Zbl 1428.52004Brandenberg, René; González Merino, Bernardo; Jahn, Thomas; Martini, Horst 4 2019 The Rosenthal-Szasz inequality for normed planes. Zbl 1406.52004Balestro, Vitor; Martini, Horst 3 2019 The inverse problem on roulettes in normed planes. Zbl 1452.46012Balestro, Vitor; Horváth, Ákos G.; Martini, Horst 1 2019 Optimal constants in normed planes. Zbl 1420.46015Balestro, Vitor; Martini, Horst; Teixeira, Ralph 1 2019 On self-circumferences in Minkowski planes. Zbl 1427.52007Ghandehari, Mostafa; Martini, Horst 1 2019 Bipartite sets of spheres and Casey-type theorems. Zbl 1409.51016Maehara, Hiroshi; Martini, Horst 1 2019 On Legendre curves in normed planes. Zbl 1408.46017Balestro, Vitor; Martini, Horst; Teixeira, Ralph 4 2018 Monge points, Euler lines, and Feuerbach spheres in Minkowski spaces. Zbl 1415.51030Leopold, Undine; Martini, Horst 2 2018 An analogue of Sylvester’s four-point problem on the sphere. Zbl 1449.60013Maehara, H.; Martini, H. 2 2018 A synthetic way to geometrize the method of coordinates. Zbl 1404.51015Anatriello, Giuseppina; Martini, Horst; Vincenzi, Giovanni 1 2018 On the Erdős-Mordell inequality for normed planes and spaces. Zbl 1413.46018Ghandehari, Mostafa; Martini, Horst 1 2018 Angles in normed spaces. Zbl 1365.52006Balestro, Vitor; Horváth, Ákos G.; Martini, Horst; Teixeira, Ralph 18 2017 Geometric properties of a sine function extendable to arbitrary normed planes. Zbl 1367.52005Balestro, Vitor; Martini, Horst; Teixeira, Ralph 12 2017 Ball convex bodies in Minkowski spaces. Zbl 1378.46015Jahn, Thomas; Martini, Horst; Richter, Christian 6 2017 On Lexell’s theorem. Zbl 1391.51017Maehara, Hiroshi; Martini, Horst 4 2017 Angle measures, general rotations, and roulettes in normed planes. Zbl 1388.46016Balestro, Vitor; Horváth, Ákos G.; Martini, Horst 4 2017 Outer normal transforms of convex polytopes. Zbl 1378.52012Maehara, Hiroshi; Martini, Horst 2 2017 Geometric probability on the sphere. Zbl 1401.60019Maehara, Hiroshi; Martini, Horst 2 2017 New inequalities for products of cross-section measures. Zbl 1377.52006Martini, Horst; Mustafaev, Zokhrab 2 2017 New moduli for Banach spaces. Zbl 1379.46018Ivanov, G.; Martini, H. 2 2017 Holding convex polyhedra by circular rings. Zbl 1406.52006Maehara, Hiroshi; Martini, Horst 1 2017 Locally 3-transitive graphs of girth 4. Zbl 1359.05032Perles, Micha A.; Martini, Horst; Kupitz, Yaakov S. 1 2017 Geometric constants for quantifying the difference between orthogonality types. Zbl 1365.46012Balestro, Vitor; Martini, Horst; Teixeira, Ralph 10 2016 A new construction of Radon curves and related topics. Zbl 1372.52004Balestro, Vitor; Martini, Horst; Teixeira, Ralph 8 2016 Involutes of polygons of constant width in Minkowski planes. Zbl 1354.52003Craizer, Marcos; Martini, Horst 7 2016 Bi- and multifocal curves and surfaces for gauges. Zbl 1348.51006Jahn, Thomas; Martini, Horst; Richter, Christian 6 2016 Polygons derived from polygons via iterated constructions. Zbl 1341.51016Donisi, Serena; Martini, Horst; Vincenzi, Giovanni; Vitale, Gaetano 5 2016 More characterizations of certain special families of simplices. Zbl 1335.52024Hajja, M.; Hayajneh, M.; Martini, H. 4 2016 On covering functionals of convex bodies. Zbl 1334.52007He, Chan; Martini, Horst; Wu, Senlin 4 2016 Minsum location extended to gauges and to convex sets. Zbl 1329.52010Jahn, Thomas; Kupitz, Yaakov S.; Martini, Horst; Richter, Christian 9 2015 Complete sets need not be reduced in Minkowski spaces. Zbl 1347.52008Martini, Horst; Wu, Senlin 4 2015 Orthogonalities, transitivity of norms and characterizations of Hilbert spaces. Zbl 1322.46009Martini, Horst; Wu, Senlin 4 2015 Algorithms for ball hulls and ball intersections in normed planes. Zbl 1408.52025Martín, Pedro; Martini, Horst 2 2015 Centered convex bodies and inequalities for cross-section measures. Zbl 1331.52007Martini, Horst; Mustafaev, Zokhrab 1 2015 Reduced convex bodies in finite dimensional normed spaces: a survey. Zbl 1310.52004Lassak, Marek; Martini, Horst 12 2014 Classical curve theory in normed planes. Zbl 1364.52005Martini, Horst; Wu, Senlin 9 2014 Geometric algebra of strictly convex Minkowski planes. Zbl 1320.46015Martini, Horst; Spirova, Margarita; Strambach, Karl 7 2014 Chebyshev sets and ball operators. Zbl 1303.41014Martín, Pedro; Martini, Horst; Spirova, Margarita 6 2014 Illuminating and covering convex bodies. Zbl 1303.52009Martini, Horst; Richter, Christian; Spirova, Margarita 5 2014 On translative coverings of convex bodies. Zbl 1305.52022Lassak, Marek; Martini, Horst; Spirova, Margarita 3 2014 Complete sets and completion of sets in Banach spaces. Zbl 1311.46015Martini, Horst; Papini, Pier Luigi; Spirova, Margarita 2 2014 Characterizations of \(l_\infty^n\) and \(l_1^n\), and their stabilities. Zbl 1294.52006Martini, Horst; Wu, Senlin 1 2014 Dispensable points, radial functions, and boundaries of starshaped sets. Zbl 1340.52002Hansen, Guillermo; Martini, Horst 1 2014 Rotation indices related to Poncelet’s closure theorem. Zbl 1312.51005Cieślak, Waldemar; Martini, Horst; Mozgawa, Witold 1 2014 On a theorem of D. Ryabogin and V. Yaskin about detecting symmetry. Zbl 1381.52011Makai, E. jun.; Martini, H.; Ódor, T. 1 2014 The Fermat-Torricelli problem. I: A discrete gradient-method approach. Zbl 1292.90282Kupitz, Yaakov S.; Martini, Horst; Spirova, Margarita 7 2013 Orthocentric simplices as the true generalizations of triangles. Zbl 1287.51011Hajja, Mowaffaq; Martini, Horst 7 2013 On the rotation index of bar billiards and Poncelet’s porism. Zbl 1278.53006Cieślak, W.; Martini, H.; Mozgawa, W. 6 2013 Intersections of balls and sets of constant width in finite-dimensional normed spaces. Zbl 1278.52002Martini, Horst; Richter, Christian; Spirova, Margarita 5 2013 On bisectors for convex distance functions. Zbl 1302.46012He, Chan; Martini, Horst; Wu, Senlin 4 2013 Bounded representation and radial projections of bisectors in normed spaces. Zbl 1273.46005Horváth, Á. G.; Martini, H. 4 2013 Cassini curves in normed planes. Zbl 1276.52008Martini, Horst; Wu, Senlin 3 2013 On reduced triangles in normed planes. Zbl 1296.46011Alonso, Javier; Martini, Horst; Spirova, Margarita 3 2013 Proposition 21 of Book I of Euclid’s Elements: variants, generalizations, and open questions. Zbl 1303.51010Hajja, Mowaffaq; Martini, Horst 2 2013 Concurrency of the altitudes of a triangle. Zbl 1291.51012Hajja, Mowaffaq; Martini, Horst 1 2013 On the polygonal diameter (= link diameter) of the interior, resp. exterior, of a simple closed polygon in the plane. Zbl 1294.52003Perles, Micha A.; Martini, Horst; Kupitz, Yaakov S. 1 2013 Locally symmetric graphs of girth 4. Zbl 1264.05087Perles, Micha A.; Martini, Horst; Kupitz, Yaakov S. 1 2013 On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces. Zbl 1241.46006Alonso, Javier; Martini, Horst; Wu, Senlin 102 2012 Minimal enclosing discs, circumcircles, and circumcenters in normed planes. I. Zbl 1245.65022Alonso, Javier; Martini, Horst; Spirova, Margarita 14 2012 Minimal enclosing discs, circumcircles, and circumcenters in normed planes. II. Zbl 1251.65016Alonso, Javier; Martini, Horst; Spirova, Margarita 13 2012 On Zindler curves in normed planes. Zbl 1276.52007Martini, Horst; Wu, Senlin 8 2012 Centrally symmetric convex bodies and sections having maximal quermassintegrals. Zbl 1265.52005Makai, E. jun.; Martini, H. 3 2012 Minsum hyperspheres in normed spaces. Zbl 1250.90049Körner, Mark-Christoph; Martini, Horst; Schöbel, Anita 3 2012 On unit balls and isoperimetrices in normed spaces. Zbl 1259.46009Martini, Horst; Mustafaev, Zokhrab 2 2012 Reduced convex bodies in Euclidean space – a survey. Zbl 1213.52006Lassak, Marek; Martini, Horst 14 2011 Starshapedness vs. convexity. Zbl 1218.52004Hansen, Guillermo; Martini, Horst 6 2011 Conics in normed planes. Zbl 1266.46011Horváth, Ákos G.; Martini, Horst 6 2011 On orthogonal chords in normed planes. Zbl 1214.52001Alonso, Javier; Martini, Horst; Mustafaev, Zokhrab 5 2011 An integral formula related to inner isoptics. Zbl 1252.52003Martini, Horst; Mozgawa, Witold 4 2011 Geometry where direction matters – or does it? Zbl 1233.52005Martini, Horst; Spirova, Margarita; Swanepoel, Konrad J. 2 2011 On the self-perimeter of quadrangles for gauges. Zbl 1222.52001Martini, H.; Shcherba, A. 1 2011 Ball polytopes and the Vázsonyi problem. Zbl 1224.52025Kupitz, Y. S.; Martini, H.; Perles, M. A. 15 2010 On closed starshaped sets. Zbl 1207.52006Hansen, Guillermo; Martini, Horst 4 2010 Tangent segments and orthogonality types in normed planes. Zbl 1228.51020Martini, Horst; Wu, Senlin 3 2010 On isoperimetric inequalities in Minkowski spaces. Zbl 1196.52007Martini, Horst; Mustafaev, Zokhrab 3 2010 Concurrent and parallel chords of spheres in normed linear spaces. Zbl 1240.46049Martini, Horst; Wu, Senlin 2 2010 Minkowskian rhombi and squares inscribed in convex Jordan curves. Zbl 1213.52001Martini, Horst; Wu, Senlin 2 2010 Golden rectangles in normed planes. Zbl 1226.46013Martini, Horst; Spirova, Margarita 2 2010 A new type of orthogonality for normed planes. Zbl 1224.46026Martini, Horst; Spirova, Margarita 2 2010 On angular bisectors in normed linear spaces. Zbl 1239.46019Martini, Horst; Wu, Senlin 1 2010 On maps preserving isosceles orthogonality in normed linear spaces. Zbl 1216.46008Martini, Horst; Wu, Senlin 7 2009 Reflections in strictly convex Minkowski planes. Zbl 1214.52002Martini, Horst; Spirova, Margarita 6 2009 On the circular hull property in normed planes. Zbl 1212.46032Martini, H.; Spirova, M. 5 2009 Geometric dilation of closed curves in normed planes. Zbl 1161.65014Martini, Horst; Wu, Senlin 5 2009 On orthocentric systems in strictly convex normed planes. Zbl 1196.52003Martini, Horst; Wu, Senlin 5 2009 On regular 4-coverings and their application for lattice coverings in normed planes. Zbl 1186.52007Martini, Horst; Spirova, Margarita 4 2009 Characterizations of central symmetry for convex bodies in Minkowski space. Zbl 1224.52007Averkov, Gennadiy; Makai, Endre jun.; Martini, Horst 3 2009 A Jordan-Brouwer separation theorem for polyhedral pseudomanifolds. Zbl 1176.52005Perles, Micha A.; Martini, Horst; Kupitz, Yaakov S. 3 2009 Minimum chords in Minkowski planes. Zbl 1181.46006Martini, Horst; Wu, Senlin 3 2009 Covering discs in Minkowski planes. Zbl 1184.52019Martini, Horst; Spirova, Margarita 3 2009 ...and 114 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 704 Authors 110 Martini, Horst 25 Balestro, Vitor 23 Wu, Senlin 19 Hajja, Mowaffaq 19 Spirova, Margarita Georgieva 18 Swanepoel, Konrad J. 15 Tanaka, Ryotaro 15 Teixeira, Ralph Costa 14 Raĭgorodskiĭ, Andreĭ Mikhaĭlovich 12 Lassak, Marek 12 Zachos, Anastasios N. 11 Horváth, Ákos G. 11 Schöbel, Anita 10 He, Chan 10 Mozgawa, Witold 9 Bezdek, Károly 9 Cheng, Raymond 9 Jahn, Thomas 9 Kupitz, Yaakov S. 9 Lángi, Zsolt 8 Alonso, Javier 8 Hayajneh, Mostafa 8 Merino, Bernardo González 8 Moreno, José-Pedro 8 Nam, Nguyen Mau 8 Sain, Debmalya 8 Saito, Kichisuke 8 Soltan, Valeriu 7 Brandenberg, René 7 Maehara, Hiroshi 7 Naszódi, Márton 7 Richter, Christian 6 Boltyanskij, Vladimir Grigor’evich 6 Komuro, Naoto 6 Kurusa, Árpád 6 Schulte, Egon 5 Cieślak, Waldemar 5 Fodor, Ferenc 5 Jin, Hailin 5 Mustafaev, Zokhrab 5 Papini, Pier Luigi 5 Plastria, Frank 5 Polyanskiĭ, Aleksandr Andreevich 5 Ross, William T. 5 Schneider, Rolf G. 5 Vincenzi, Giovanni 5 Wójcik, Paweł 5 Zamani, Ali 5 Zong, Chuanming 4 Bisztriczky, Tibor 4 Bottazzi, Tamara 4 Brazil, Marcus N. 4 Breen, Marilyn 4 Cabello Sánchez, Javier 4 Craizer, Marcos 4 Di Stefano, Gabriele 4 Gunawan, Hendra 4 Hammoudeh, Ismail 4 Kupavskii, Andrey 4 Leng, Gangsong 4 Moslehian, Mohammad Sal 4 Navarra, Alfredo 4 Pach, János 4 Paul, Kallol 4 Perles, Micha A. 4 Pushnyakov, Filipp Anatol’evich 4 Pyaderkin, M. M. 4 Ras, Charl J. 4 Saleh, Wedad 4 Skrzypiec, Magdalena 4 Thomas, Doreen Anne 4 Väisälä, Jussi 4 Weiß, Gunter 4 Wenzel, Walter 4 Xi, Lifeng 3 Alimov, Alexey R. 3 An, Nguyen Thai 3 Arambašić, Ljiljana 3 Averkov, Gennadiy 3 Azhmyakov, Vadim 3 Berele, Allan 3 Brimberg, Jack 3 Catoiu, Stefan 3 Chen, Chen 3 Chmieliński, Jacek 3 Conde, Cristian M. 3 Edmonds, Allan L. 3 Filliman, Paul 3 Hug, Daniel 3 Kiliçman, Adem 3 Körner, Mark-Christoph 3 Kozma, József 3 Laudano, Francesco 3 Li, Yongjin 3 Ma, Ying 3 Makai, Endre jun. 3 Mashreghi, Javad 3 Mizuguchi, Hiroyasu 3 Monson, Barry 3 Montejano Peimbert, Luis ...and 604 more Authors all top 5 Cited in 189 Serials 73 Beiträge zur Algebra und Geometrie 37 Aequationes Mathematicae 32 Journal of Mathematical Analysis and Applications 31 Discrete & Computational Geometry 29 Journal of Geometry 21 Results in Mathematics 20 Journal of Optimization Theory and Applications 16 Mathematical Notes 16 Linear Algebra and its Applications 13 Mathematika 12 Advances in Mathematics 12 Journal of Convex Analysis 11 Discrete Mathematics 11 Periodica Mathematica Hungarica 10 Computational Geometry 9 Israel Journal of Mathematics 9 Monatshefte für Mathematik 9 Transactions of the American Mathematical Society 9 Advances in Geometry 8 Mediterranean Journal of Mathematics 7 Archiv der Mathematik 7 Geometriae Dedicata 7 Proceedings of the American Mathematical Society 7 European Journal of Operational Research 7 Expositiones Mathematicae 6 Acta Mathematica Hungarica 6 Journal of Mathematical Sciences (New York) 6 Doklady Mathematics 5 Discrete Applied Mathematics 5 Journal of Inequalities and Applications 5 Annals of Functional Analysis 4 Bulletin of the Australian Mathematical Society 4 Mathematische Semesterberichte 4 Rocky Mountain Journal of Mathematics 4 The Mathematical Intelligencer 4 Journal of Combinatorial Theory. 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Mathematica 1 Automatica 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Collectanea Mathematica 1 Czechoslovak Mathematical Journal 1 Demonstratio Mathematica 1 Glasgow Mathematical Journal ...and 89 more Serials all top 5 Cited in 46 Fields 400 Convex and discrete geometry (52-XX) 175 Functional analysis (46-XX) 167 Geometry (51-XX) 62 Differential geometry (53-XX) 62 Operations research, mathematical programming (90-XX) 61 Combinatorics (05-XX) 27 Operator theory (47-XX) 24 Computer science (68-XX) 22 Numerical analysis (65-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 17 Real functions (26-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 14 Probability theory and stochastic processes (60-XX) 12 General topology (54-XX) 11 Functions of a complex variable (30-XX) 10 Approximations and expansions (41-XX) 10 Statistics (62-XX) 8 Algebraic geometry (14-XX) 8 Measure and integration (28-XX) 8 Difference and functional equations (39-XX) 7 Mathematics education (97-XX) 6 History and biography (01-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Number theory (11-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Systems theory; control (93-XX) 4 Group theory and generalizations (20-XX) 4 Partial differential equations (35-XX) 4 Information and communication theory, circuits (94-XX) 3 Ordinary differential equations (34-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Manifolds and cell complexes (57-XX) 3 Geophysics (86-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Field theory and polynomials (12-XX) 2 Potential theory (31-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Algebraic topology (55-XX) 2 Mechanics of deformable solids (74-XX) 1 General and overarching topics; collections (00-XX) 1 Topological groups, Lie groups (22-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) Citations by Year