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Homepage: https://www.tu-chemnitz.de/mathematik/geometrie/index.php External Links: MGP · dblp · GND Documents Indexed: 281 Publications since 1984, including 4 Books Reviewing Activity: 483 Reviews Biographic References: 1 Publication all top 5 Co-Authors 33 single-authored 30 Spirova, Margarita Georgieva 28 Kupitz, Yaakov S. 23 Wu, Senlin 20 Balestro, Vitor 16 Makai, Endre jun. 14 Boltyanskij, Vladimir Grigor’evich 13 Teixeira, Ralph C. 12 Maehara, Hiroshi 12 Mustafaev, Zokhrab 12 Swanepoel, Konrad J. 11 Hajja, Mowaffaq 11 Perles, Micha A. 11 Soltan, Valeriu 8 Wenzel, Walter 7 Alonso, Javier 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 Körner, Mark-Christoph 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 12 Aequationes Mathematicae 9 Periodica Mathematica Hungarica 9 Geometriae Dedicata 8 Journal of Geometry 8 Studia Scientiarum Mathematicarum Hungarica 7 Discrete Mathematics 7 Journal of Convex Analysis 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 Journal of Graph Theory 3 Mathematika 3 Publicationes Mathematicae 3 European Journal of Combinatorics 3 Note di Matematica 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 Mathematische Semesterberichte 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 Graphs and Combinatorics 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 220 Convex and discrete geometry (52-XX) 88 Geometry (51-XX) 79 Functional analysis (46-XX) 26 Differential geometry (53-XX) 15 Combinatorics (05-XX) 12 Operations research, mathematical programming (90-XX) 9 History and biography (01-XX) 9 Computer science (68-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) 2 Measure and integration (28-XX) 2 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-XX) 2 Global analysis, analysis on manifolds (58-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 Approximations and expansions (41-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 202 Publications have been cited 1,346 times in 629 Documents Cited by ▼ Year ▼ The geometry of Minkowski spaces – a survey. I. Zbl 0984.52004Martini, Horst; Swanepoel, Konrad J.; Weiß, Gunter 96 2001 On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces. Zbl 1241.46006Alonso, Javier; Martini, Horst; Wu, Senlin 83 2012 Excursions into combinatorial geometry. Zbl 0877.52001Boltyanski, V.; Martini, H.; Soltan, Petru S. 82 1997 The geometry of Minkowski spaces – a survey. II. Zbl 1080.52005Martini, H.; Swanepoel, K. J. 72 2004 Geometric methods and optimization problems. Zbl 0933.90002Boltyanski, V.; Martini, H.; Soltan, V. 44 1999 Antinorms and Radon curves. Zbl 1108.52005Martini, Horst; Swanepoel, Konrad J. 40 2006 Combinatorial problems on the illumination of convex bodies. Zbl 0937.52006Martini, Horst; Soltan, Valeriu 38 1999 Geometric aspects of the generalized Fermat-Torricelli problem. Zbl 0911.51021Kupitz, Y. S.; Martini, H. 36 1997 Special convex bodies. Zbl 0794.52002Heil, E.; Martini, H. 36 1993 The Fermat–Torricelli problem in normed planes and spaces. Zbl 1047.90032Martini, H.; Swanepoel, K. J.; Weiss, G. 26 2002 Orthocentric simplices and their centers. Zbl 1084.51008Edmonds, Allan L.; Hajja, Mowaffaq; Martini, Horst 14 2005 Hyperplane approximation and related topics. Zbl 0809.52013Korneenko, Nikolai M.; Martini, Horst 14 1993 On the theorem of Napoleon and related topics. Zbl 0864.51009Martini, Horst 13 1996 Antipodality properties of finite sets in Euclidean space. Zbl 1066.52010Martini, H.; Soltan, V. 13 2005 Minimal enclosing discs, circumcircles, and circumcenters in normed planes. I. Zbl 1245.65022Alonso, Javier; Martini, Horst; Spirova, Margarita 13 2012 Ball polytopes and the Vázsonyi problem. Zbl 1224.52025Kupitz, Y. S.; Martini, H.; Perles, M. A. 13 2010 Angles in normed spaces. Zbl 1365.52006Balestro, Vitor; Horváth, Ákos G.; Martini, Horst; Teixeira, Ralph 13 2017 Bodies of constant width. An introduction to convex geometry with applications. Zbl 1468.52001Martini, Horst; Montejano, Luis; Oliveros, Déborah 13 2019 Minimal enclosing discs, circumcircles, and circumcenters in normed planes. II. Zbl 1251.65016Alonso, Javier; Martini, Horst; Spirova, Margarita 12 2012 Reduced convex bodies in Euclidean space – a survey. Zbl 1213.52006Lassak, Marek; Martini, Horst 12 2011 The Feuerbach circle and orthocentricity in normed places. Zbl 1144.52001Martini, Horst; Spirova, Margarita 12 2007 The cross-section body, plane sections of convex bodies and approximation of convex bodies. I. Zbl 0865.52005Makai, E. jun.; Martini, H. 11 1996 Coincidences of simplex centers and related facial structures. Zbl 1093.51014Edmonds, Allan L.; Hajja, Mowaffaq; Martini, Horst 11 2005 Reduced bodies in Minkowski space. Zbl 1084.52004Lassak, M.; Martini, H. 11 2005 Maximal sections and centrally symmetric bodies. Zbl 1012.52008Makai, E. jun.; Martini, H.; Ódor, T. 10 2000 The Fermat-Torricelli point and isosceles tetrahedra. Zbl 0795.51006Kupitz, Yaakov S.; Martini, Horst 10 1994 Median hyperplanes in normed spaces – a survey. Zbl 0921.90109Martini, Horst; Schöbel, Anita 10 1998 Geometric properties of a sine function extendable to arbitrary normed planes. Zbl 1367.52005Balestro, Vitor; Martini, Horst; Teixeira, Ralph 10 2017 Median and center hyperplanes in Minkowski spaces – a unified approach. Zbl 1010.51002Martini, H.; Schöbel, A. 9 2001 Reduced convex bodies in finite dimensional normed spaces: a survey. Zbl 1310.52004Lassak, Marek; Martini, Horst 9 2014 Illumination and visibility problems in terms of closure operators. Zbl 1074.52001Martini, Horst; Wenzel, Walter 8 2004 Geometric constants for quantifying the difference between orthogonality types. Zbl 1365.46012Balestro, Vitor; Martini, Horst; Teixeira, Ralph 8 2016 Classical curve theory in normed planes. Zbl 1364.52005Martini, Horst; Wu, Senlin 8 2014 Napoleon’s theorem with weights in \(n\)-space. Zbl 0920.51008Martini, H.; Weißbach, B. 8 1999 On converses of Napoleon’s theorem and a modified shape function. Zbl 1116.51013Hajja, Mowaffaq; Martini, Horst; Spirova, Margarita 8 2006 New extensions of Napoleon’s theorem to higher dimensions. Zbl 1142.51015Hajja, Mowaffaq; Martini, Horst; Spirova, Margarita 8 2008 On reduced polytopes and antipodality. Zbl 1158.52012Averkov, Gennadiy; Martini, Horst 8 2008 A hierarchical classification of Euclidean polytopes with regularity properties. Zbl 0812.51015Martini, Horst 7 1994 Orthocentric simplices as the true generalizations of triangles. Zbl 1287.51011Hajja, Mowaffaq; Martini, Horst 7 2013 Approximating finite weighted point sets by hyperplanes. Zbl 0703.68097Korneenko, N. M.; Martini, H. 7 1990 On maps preserving isosceles orthogonality in normed linear spaces. Zbl 1216.46008Martini, Horst; Wu, Senlin 7 2009 Orthocentric simplices and biregularity. Zbl 1146.51016Edmonds, Allan L.; Hajja, Mowaffaq; Martini, Horst 7 2008 Minsum location extended to gauges and to convex sets. Zbl 1329.52010Jahn, Thomas; Kupitz, Yaakov S.; Martini, Horst; Richter, Christian 7 2015 The Fermat-Torricelli problem. I: A discrete gradient-method approach. Zbl 1292.90282Kupitz, Yaakov S.; Martini, Horst; Spirova, Margarita 7 2013 Radial projections of bisectors in Minkowski spaces. Zbl 1158.52007Martini, Horst; Wu, Senlin 7 2008 Generalized convexity notions and combinatorial geometry. Zbl 1051.52004Martini, H.; Swanepoel, K. J. 6 2003 Non-planar simplices are not reduced. Zbl 1048.52002Martini, H.; Swanepoel, K. J. 6 2004 Equiframed curves – a generalization of Radon curves. Zbl 1071.52002Martini, Horst; Swanepoel, Konrad J. 6 2004 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 Recent results in elementary geometry. II. Zbl 0852.51013Martini, Horst 6 1995 Geometric algebra of strictly convex Minkowski planes. Zbl 1320.46015Martini, Horst; Spirova, Margarita; Strambach, Karl 6 2014 A new construction of Radon curves and related topics. Zbl 1372.52004Balestro, Vitor; Martini, Horst; Teixeira, Ralph 6 2016 On the isoperimetric inequalities for Reuleaux polygons. Zbl 0956.51011Kupitz, Yaakov S.; Martini, Horst 6 2000 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. 6 1991 Cross-sectional measures. Zbl 0820.52003Martini, H. 6 1994 Reflections in strictly convex Minkowski planes. Zbl 1214.52002Martini, Horst; Spirova, Margarita 6 2009 Jung’s theorem for a pair of Minkowski spaces. Zbl 1151.52006Boltyanski, Vladimir; Martini, Horst 6 2006 Symmetrization of closure operators and visibility. Zbl 1099.06003Martini, Horst; Wenzel, Walter 6 2005 Clifford’s chain of theorems in strictly convex Minkowski planes. Zbl 1174.51005Martini, Horst; Spirova, Margarita 6 2008 A characterization of convex sets via visibility. Zbl 1013.52005Martini, H.; Wenzel, W. 5 2002 Two characterizations of smooth norms. Zbl 0952.52006Martini, H.; Schöbel, A. 5 1999 Shadow-boundaries of convex bodies. Zbl 0863.52003Martini, Horst 5 1996 A linear-time construction of Reuleaux polygons. Zbl 0876.52002Kupitz, Yaakov; Martini, Horst; Wegner, Bernd 5 1996 An analogue of the Krein-Milman theorem for star-shaped sets. Zbl 1043.52006Martini, Horst; Wenzel, Walter 5 2003 Chebyshev sets and ball operators. Zbl 1303.41014Martín, Pedro; Martini, Horst; Spirova, Margarita 5 2014 Illuminating and covering convex bodies. Zbl 1303.52009Martini, Horst; Richter, Christian; Spirova, Margarita 5 2014 Bi- and multifocal curves and surfaces for gauges. Zbl 1348.51006Jahn, Thomas; Martini, Horst; Richter, Christian 5 2016 Convex polytopes whose projection bodies and difference sets are polars. Zbl 0679.52002Martini, Horst 5 1991 Star-shaped sets in normed spaces. Zbl 0847.52003Boltyanski, V.; Martini, H.; Soltan, P. S. 5 1996 On the circular hull property in normed planes. Zbl 1212.46032Martini, H.; Spirova, M. 5 2009 Starshapedness vs. convexity. Zbl 1218.52004Hansen, Guillermo; Martini, Horst 5 2011 Zur besten Beleuchtung konvexer Polyeder. Zbl 0543.52014Martini, Horst; Weißbach, Bernulf 5 1984 Low-degree minimal spanning trees in normed spaces. Zbl 1105.46010Martini, Horst; Swanepoel, Konrad J. 5 2006 Finite sets in \(\mathbb R^d\) with many diameters – a survey. Zbl 1141.51300Kupitz, Y. S.; Martini, H.; Perles, M. A. 5 2005 Surface immersions in normed spaces from the affine point of view. Zbl 1427.53010Balestro, Vitor; Martini, Horst; Teixeira, Ralph 5 2019 On the rotation index of bar billiards and Poncelet’s porism. Zbl 1278.53006Cieślak, W.; Martini, H.; Mozgawa, W. 5 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 bodies associated with a given convex body. Zbl 0884.52005Makai, Endre jun.; Martini, Horst 4 1996 Tetrahedra are not reduced. Zbl 1018.52006Martini, H.; Wenzel, W. 4 2002 Regular polytopes and generalizations. (Reguläre Polytope und Verallgemeinerungen.) Zbl 0810.52011Martini, Horst 4 1994 Ball convex bodies in Minkowski spaces. Zbl 1378.46015Jahn, Thomas; Martini, Horst; Richter, Christian 4 2017 Involutes of polygons of constant width in Minkowski planes. Zbl 1354.52003Craizer, Marcos; Martini, Horst 4 2016 More characterizations of certain special families of simplices. Zbl 1335.52024Hajja, M.; Hayajneh, M.; Martini, H. 4 2016 Polygons derived from polygons via iterated constructions. Zbl 1341.51016Donisi, Serena; Martini, Horst; Vincenzi, Giovanni; Vitale, Gaetano 4 2016 Some results and problems around zonotopes. Zbl 0634.52007Martini, H. 4 1987 Carathéodory’s theorem and \(H\)-convexity. Zbl 0976.52007Boltyanski, V.; Martini, H. 4 2001 Some characterizing properties of the simplex. Zbl 0674.52005Martini, Horst 4 1989 A new view on some characterizations of simplices. Zbl 0679.52003Martini, Horst 4 1990 A new characterization of convex plates of constant width. Zbl 0688.52002Makai, Endre jun.; Martini, Horst 4 1990 Cassini curves in light field theory. (Cassini-Kurven in der Lichtfeldtheorie.) Zbl 0762.51011Martini, Horst; Schiel, Uwe 4 1992 Minimum convex partition of polygonal domains by guillotine cuts. Zbl 0901.52014Martini, H.; Soltan, V. 4 1998 The cross-section body, plane sections of convex bodies and approximation of convex bodies. II. Zbl 0914.52002Makai, E. jun.; Martini, H. 4 1998 A new construction of curves of constant width. Zbl 1172.51309Martini, Horst; Mustafaev, Zokhrab 4 2008 Circle geometry in affine Cayley-Klein planes. Zbl 1199.51013Martini, Horst; Spirova, Margarita 4 2008 On orthocentric systems in strictly convex normed planes. Zbl 1196.52003Martini, Horst; Wu, Senlin 4 2009 On closed starshaped sets. Zbl 1207.52006Hansen, Guillermo; Martini, Horst 4 2010 On Reuleaux triangles in Minkowski planes. Zbl 1121.52006Martini, Horst; Mustafaev, Zokhrab 4 2007 On orthogonal chords in normed planes. Zbl 1214.52001Alonso, Javier; Martini, Horst; Mustafaev, Zokhrab 4 2011 Orthogonalities, transitivity of norms and characterizations of Hilbert spaces. Zbl 1322.46009Martini, Horst; Wu, Senlin 4 2015 Zur Bestimmung konvexer Polytope durch die Inhalte ihrer Projektionen. Zbl 0544.52005Martini, Horst 4 1984 Curvature types of planar curves for gauges. Zbl 1452.46013Balestro, Vitor; Martini, Horst; Sakaki, Makoto 1 2020 On curvature of surfaces immersed in normed spaces. Zbl 1452.53005Balestro, Vitor; Martini, Horst; Teixeira, Ralph 1 2020 Starshaped sets. Zbl 1454.52001Hansen, G.; Herburt, I.; Martini, H.; Moszyńska, M. 1 2020 Bodies of constant width. An introduction to convex geometry with applications. Zbl 1468.52001Martini, Horst; Montejano, Luis; Oliveros, Déborah 13 2019 Surface immersions in normed spaces from the affine point of view. Zbl 1427.53010Balestro, Vitor; Martini, Horst; Teixeira, Ralph 5 2019 Concepts of curvatures in normed planes. Zbl 1432.52001Balestro, Vitor; Martini, Horst; Shonoda, Emad 3 2019 The Rosenthal-Szasz inequality for normed planes. Zbl 1406.52004Balestro, Vitor; Martini, Horst 1 2019 Bipartite sets of spheres and Casey-type theorems. Zbl 1409.51016Maehara, Hiroshi; Martini, Horst 1 2019 Is a complete, reduced set necessarily of constant width? Zbl 1428.52004Brandenberg, René; Merino, Bernardo González; Jahn, Thomas; Martini, Horst 1 2019 An analogue of Sylvester’s four-point problem on the sphere. Zbl 1449.60013Maehara, H.; Martini, H. 2 2018 On the Erdős-Mordell inequality for normed planes and spaces. Zbl 1413.46018Ghandehari, Mostafa; Martini, Horst 1 2018 On Legendre curves in normed planes. Zbl 1408.46017Balestro, Vitor; Martini, Horst; Teixeira, Ralph 1 2018 Angles in normed spaces. Zbl 1365.52006Balestro, Vitor; Horváth, Ákos G.; Martini, Horst; Teixeira, Ralph 13 2017 Geometric properties of a sine function extendable to arbitrary normed planes. Zbl 1367.52005Balestro, Vitor; Martini, Horst; Teixeira, Ralph 10 2017 Ball convex bodies in Minkowski spaces. Zbl 1378.46015Jahn, Thomas; Martini, Horst; Richter, Christian 4 2017 Angle measures, general rotations, and roulettes in normed planes. Zbl 1388.46016Balestro, Vitor; Horváth, Ákos G.; Martini, Horst 3 2017 On Lexell’s theorem. Zbl 1391.51017Maehara, Hiroshi; Martini, Horst 3 2017 Outer normal transforms of convex polytopes. Zbl 1378.52012Maehara, Hiroshi; Martini, Horst 2 2017 New inequalities for products of cross-section measures. Zbl 1377.52006Martini, Horst; Mustafaev, Zokhrab 1 2017 New moduli for Banach spaces. Zbl 1379.46018Ivanov, G.; Martini, H. 1 2017 Geometric probability on the sphere. Zbl 1401.60019Maehara, Hiroshi; Martini, Horst 1 2017 Holding convex polyhedra by circular rings. Zbl 1406.52006Maehara, Hiroshi; Martini, Horst 1 2017 Geometric constants for quantifying the difference between orthogonality types. Zbl 1365.46012Balestro, Vitor; Martini, Horst; Teixeira, Ralph 8 2016 A new construction of Radon curves and related topics. Zbl 1372.52004Balestro, Vitor; Martini, Horst; Teixeira, Ralph 6 2016 Bi- and multifocal curves and surfaces for gauges. Zbl 1348.51006Jahn, Thomas; Martini, Horst; Richter, Christian 5 2016 Involutes of polygons of constant width in Minkowski planes. Zbl 1354.52003Craizer, Marcos; Martini, Horst 4 2016 More characterizations of certain special families of simplices. Zbl 1335.52024Hajja, M.; Hayajneh, M.; Martini, H. 4 2016 Polygons derived from polygons via iterated constructions. Zbl 1341.51016Donisi, Serena; Martini, Horst; Vincenzi, Giovanni; Vitale, Gaetano 4 2016 On covering functionals of convex bodies. Zbl 1334.52007He, Chan; Martini, Horst; Wu, Senlin 3 2016 Minsum location extended to gauges and to convex sets. Zbl 1329.52010Jahn, Thomas; Kupitz, Yaakov S.; Martini, Horst; Richter, Christian 7 2015 Orthogonalities, transitivity of norms and characterizations of Hilbert spaces. Zbl 1322.46009Martini, Horst; Wu, Senlin 4 2015 Complete sets need not be reduced in Minkowski spaces. Zbl 1347.52008Martini, Horst; Wu, Senlin 3 2015 Algorithms for ball hulls and ball intersections in normed planes. Zbl 1408.52025Martín, Pedro; Martini, Horst 2 2015 Reduced convex bodies in finite dimensional normed spaces: a survey. Zbl 1310.52004Lassak, Marek; Martini, Horst 9 2014 Classical curve theory in normed planes. Zbl 1364.52005Martini, Horst; Wu, Senlin 8 2014 Geometric algebra of strictly convex Minkowski planes. Zbl 1320.46015Martini, Horst; Spirova, Margarita; Strambach, Karl 6 2014 Chebyshev sets and ball operators. Zbl 1303.41014Martín, Pedro; Martini, Horst; Spirova, Margarita 5 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 On a theorem of D. Ryabogin and V. Yaskin about detecting symmetry. Zbl 1381.52011Makai, E. jun.; Martini, H.; Ódor, T. 1 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 Orthocentric simplices as the true generalizations of triangles. Zbl 1287.51011Hajja, Mowaffaq; Martini, Horst 7 2013 The Fermat-Torricelli problem. I: A discrete gradient-method approach. Zbl 1292.90282Kupitz, Yaakov S.; Martini, Horst; Spirova, Margarita 7 2013 On the rotation index of bar billiards and Poncelet’s porism. Zbl 1278.53006Cieślak, W.; Martini, H.; Mozgawa, W. 5 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 3 2013 Bounded representation and radial projections of bisectors in normed spaces. Zbl 1273.46005Horváth, Á. G.; Martini, H. 3 2013 Proposition 21 of Book I of Euclid’s Elements: variants, generalizations, and open questions. Zbl 1303.51010Hajja, Mowaffaq; Martini, Horst 2 2013 On reduced triangles in normed planes. Zbl 1296.46011Alonso, Javier; Martini, Horst; Spirova, Margarita 2 2013 Cassini curves in normed planes. Zbl 1276.52008Martini, Horst; Wu, Senlin 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 83 2012 Minimal enclosing discs, circumcircles, and circumcenters in normed planes. I. Zbl 1245.65022Alonso, Javier; Martini, Horst; Spirova, Margarita 13 2012 Minimal enclosing discs, circumcircles, and circumcenters in normed planes. II. Zbl 1251.65016Alonso, Javier; Martini, Horst; Spirova, Margarita 12 2012 On Zindler curves in normed planes. Zbl 1276.52007Martini, Horst; Wu, Senlin 3 2012 On unit balls and isoperimetrices in normed spaces. Zbl 1259.46009Martini, Horst; Mustafaev, Zokhrab 2 2012 Centrally symmetric convex bodies and sections having maximal quermassintegrals. Zbl 1265.52005Makai, E. jun.; Martini, H. 2 2012 Minsum hyperspheres in normed spaces. Zbl 1250.90049Körner, Mark-Christoph; Martini, Horst; Schöbel, Anita 2 2012 Reduced convex bodies in Euclidean space – a survey. Zbl 1213.52006Lassak, Marek; Martini, Horst 12 2011 Starshapedness vs. convexity. Zbl 1218.52004Hansen, Guillermo; Martini, Horst 5 2011 On orthogonal chords in normed planes. Zbl 1214.52001Alonso, Javier; Martini, Horst; Mustafaev, Zokhrab 4 2011 Conics in normed planes. Zbl 1266.46011Horváth, Ákos G.; Martini, Horst 4 2011 An integral formula related to inner isoptics. Zbl 1252.52003Martini, Horst; Mozgawa, Witold 1 2011 Geometry where direction matters – or does it? Zbl 1233.52005Martini, Horst; Spirova, Margarita; Swanepoel, Konrad J. 1 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. 13 2010 On closed starshaped sets. Zbl 1207.52006Hansen, Guillermo; Martini, Horst 4 2010 On isoperimetric inequalities in Minkowski spaces. Zbl 1196.52007Martini, Horst; Mustafaev, Zokhrab 2 2010 Tangent segments and orthogonality types in normed planes. Zbl 1228.51020Martini, Horst; Wu, Senlin 1 2010 On angular bisectors in normed linear spaces. Zbl 1239.46019Martini, Horst; Wu, Senlin 1 2010 Golden rectangles in normed planes. Zbl 1226.46013Martini, Horst; Spirova, Margarita 1 2010 A new type of orthogonality for normed planes. Zbl 1224.46026Martini, Horst; Spirova, Margarita 1 2010 Concurrent and parallel chords of spheres in normed linear spaces. Zbl 1240.46049Martini, Horst; Wu, Senlin 1 2010 Minkowskian rhombi and squares inscribed in convex Jordan curves. Zbl 1213.52001Martini, 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 On orthocentric systems in strictly convex normed planes. Zbl 1196.52003Martini, Horst; Wu, Senlin 4 2009 A Jordan-Brouwer separation theorem for polyhedral pseudomanifolds. Zbl 1176.52005Perles, Micha A.; Martini, Horst; Kupitz, Yaakov S. 3 2009 Covering discs in Minkowski planes. Zbl 1184.52019Martini, Horst; Spirova, Margarita 3 2009 On regular 4-coverings and their application for lattice coverings in normed planes. Zbl 1186.52007Martini, Horst; Spirova, Margarita 3 2009 Characterizations of central symmetry for convex bodies in Minkowski space. Zbl 1224.52007Averkov, Gennadiy; Makai, Endre jun.; Martini, Horst 3 2009 Geometric dilation of closed curves in normed planes. Zbl 1161.65014Martini, Horst; Wu, Senlin 3 2009 Minimum chords in Minkowski planes. Zbl 1181.46006Martini, Horst; Wu, Senlin 2 2009 Halving closed curves in normed planes and related inequalities. Zbl 1189.52002He, Chan; Martini, Horst; Wu, Senlin 2 2009 New extensions of Napoleon’s theorem to higher dimensions. Zbl 1142.51015Hajja, Mowaffaq; Martini, Horst; Spirova, Margarita 8 2008 On reduced polytopes and antipodality. Zbl 1158.52012Averkov, Gennadiy; Martini, Horst 8 2008 Orthocentric simplices and biregularity. Zbl 1146.51016Edmonds, Allan L.; Hajja, Mowaffaq; Martini, Horst 7 2008 Radial projections of bisectors in Minkowski spaces. Zbl 1158.52007Martini, Horst; Wu, Senlin 7 2008 Clifford’s chain of theorems in strictly convex Minkowski planes. Zbl 1174.51005Martini, Horst; Spirova, Margarita 6 2008 A new construction of curves of constant width. Zbl 1172.51309Martini, Horst; Mustafaev, Zokhrab 4 2008 Circle geometry in affine Cayley-Klein planes. Zbl 1199.51013Martini, Horst; Spirova, Margarita 4 2008 On pyramids and reducedness. Zbl 1199.52008Averkov, Gennadiy; Martini, Horst 3 2008 On the volume of the convex hull of \(d+1\) segments in \({\mathbb R}^d\). Zbl 1199.52025Averkov, Gennadiy; Martini, Horst 2 2008 Halving circular arcs in normed planes. Zbl 1199.46064Martini, Horst; Wu, Senlin 1 2008 ...and 102 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 619 Authors 104 Martini, Horst 21 Balestro, Vitor 20 Wu, Senlin 19 Spirova, Margarita Georgieva 18 Hajja, Mowaffaq 18 Swanepoel, Konrad J. 14 Raĭgorodskiĭ, Andreĭ Mikhaĭlovich 13 Teixeira, Ralph C. 12 Zachos, Anastasios N. 11 Schöbel, Anita 11 Tanaka, Ryotaro 10 Horváth, Ákos G. 10 Lassak, Marek 9 Kupitz, Yaakov S. 8 Cheng, Raymond 8 Hayajneh, Mostafa 8 He, Chan 8 Jahn, Thomas 8 Moreno, José-Pedro 8 Saito, Kichisuke 7 Alonso, Javier 7 Bezdek, Károly 7 Mozgawa, Witold 7 Nam, Nguyen Mau 7 Sain, Debmalya 7 Soltan, Valeriu 6 Boltyanskij, Vladimir Grigor’evich 6 Komuro, Naoto 6 Lángi, Zsolt 6 Maehara, Hiroshi 6 Merino, Bernardo González 6 Richter, Christian 6 Schulte, Egon 5 Brandenberg, René 5 Fodor, Ferenc 5 Jin, Hailin 5 Kurusa, Árpád 5 Naszódi, Márton 5 Polyanskiĭ, Aleksandr Andreevich 5 Ross, William T. jun. 5 Schneider, Rolf G. 5 Zamani, Ali 4 Brazil, Marcus N. 4 Breen, Marilyn 4 Cabello Sánchez, Javier 4 Cieślak, Waldemar 4 Di Stefano, Gabriele 4 Hammoudeh, Ismail 4 Kupavskii, Andrey 4 Mustafaev, Zokhrab 4 Navarra, Alfredo 4 Pach, János 4 Papini, Pier Luigi 4 Paul, Kallol 4 Perles, Micha A. 4 Pushnyakov, Filipp Anatol’evich 4 Pyaderkin, M. M. 4 Ras, Charl J. 4 Saleh, Wedad 4 Thomas, Doreen Anne 4 Väisälä, Jussi 4 Vincenzi, Giovanni 4 Weiß, Gunter 4 Wenzel, Walter 4 Wójcik, Paweł 4 Zong, Chuanming 3 An, Nguyen Thai 3 Arambašić, Ljiljana 3 Averkov, Gennadiy 3 Bottazzi, Tamara 3 Brimberg, Jack 3 Chmieliński, Jacek 3 Craizer, Marcos 3 Edmonds, Allan L. 3 Filliman, Paul 3 Gunawan, Hendra 3 Hug, Daniel 3 Kiliçman, Adem 3 Körner, Mark-Christoph 3 Laudano, Francesco 3 Leng, Gangsong 3 Makai, Endre jun. 3 Mashreghi, Javad 3 Mizuguchi, Hiroyasu 3 Monson, Barry 3 Moslehian, Mohammad Sal 3 Nicollier, Grégoire 3 Nur, Muhammad 3 Plastria, Frank 3 Rajić, Rajna 3 Röschel, Otto 3 Ryabogin, Dmitry 3 Shonoda, Emad N. 3 Thäle, Christoph 3 Tóth, Csaba D. 3 Vartziotis, Dimitris 3 Vígh, Viktor 3 Wipper, Joachim 3 Yaskin, Vladyslav 3 Zhao, Changjian ...and 519 more Authors all top 5 Cited in 165 Serials 67 Beiträge zur Algebra und Geometrie 32 Aequationes Mathematicae 29 Journal of Geometry 28 Journal of Mathematical Analysis and Applications 28 Discrete & Computational Geometry 20 Journal of Optimization Theory and Applications 20 Results in Mathematics 15 Linear Algebra and its Applications 14 Mathematical Notes 13 Mathematika 11 Periodica Mathematica Hungarica 11 Advances in Mathematics 9 Discrete Mathematics 9 Israel Journal of Mathematics 9 Monatshefte für Mathematik 9 Transactions of the American Mathematical Society 9 Computational Geometry 9 Advances in Geometry 7 Expositiones Mathematicae 6 Archiv der Mathematik 6 Geometriae Dedicata 6 Proceedings of the American Mathematical Society 6 Acta Mathematica Hungarica 6 European Journal of Operational Research 6 Journal of Mathematical Sciences (New York) 6 Journal of Convex Analysis 6 Doklady Mathematics 6 Mediterranean Journal of Mathematics 5 Discrete Applied Mathematics 4 Bulletin of the Australian Mathematical Society 4 Rocky Mountain Journal of Mathematics 4 The Mathematical Intelligencer 4 Journal of Combinatorial Theory. 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Serie Quarta 2 Applied Mathematics and Computation 2 Networks 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Pacific Journal of Mathematics 2 Rendiconti del Seminario Matematico della Università di Padova 2 Theoretical Computer Science 2 Computers & Operations Research 2 Applied Mathematics Letters 2 Science in China. Series A 2 Elemente der Mathematik 2 Distributed Computing 2 Top 2 Journal for Geometry and Graphics 2 Mathematical Inequalities & Applications 2 Journal of Geometry and Symmetry in Physics 2 Optimization Letters 2 Banach Journal of Mathematical Analysis 2 Analysis and Mathematical Physics 1 Advances in Applied Probability 1 American Mathematical Monthly 1 Archive for History of Exact Sciences 1 Inverse Problems 1 Journal of the Franklin Institute 1 Linear and Multilinear Algebra 1 Moscow University Mathematics Bulletin 1 Reports on Mathematical Physics 1 Ukrainian Mathematical Journal 1 Journal of Geometry and Physics 1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 1 Automatica 1 Canadian Journal of Mathematics 1 Collectanea Mathematica 1 Czechoslovak Mathematical Journal 1 Demonstratio Mathematica 1 Glasgow Mathematical Journal 1 Illinois Journal of Mathematics 1 Journal of Applied Probability 1 Journal of Approximation Theory 1 Journal of Economic Theory 1 Journal of Graph Theory 1 Kybernetika 1 Manuscripta Mathematica 1 Mathematische Nachrichten 1 Mathematica Slovaca ...and 65 more Serials all top 5 Cited in 45 Fields 352 Convex and discrete geometry (52-XX) 154 Functional analysis (46-XX) 143 Geometry (51-XX) 56 Operations research, mathematical programming (90-XX) 53 Combinatorics (05-XX) 51 Differential geometry (53-XX) 26 Operator theory (47-XX) 22 Numerical analysis (65-XX) 21 Computer science (68-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 13 Real functions (26-XX) 12 Probability theory and stochastic processes (60-XX) 10 General topology (54-XX) 8 Functions of a complex variable (30-XX) 7 Approximations and expansions (41-XX) 7 Statistics (62-XX) 6 History and biography (01-XX) 6 Algebraic geometry (14-XX) 6 Difference and functional equations (39-XX) 5 Partial differential equations (35-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Systems theory; control (93-XX) 5 Mathematics education (97-XX) 4 Number theory (11-XX) 4 Group theory and generalizations (20-XX) 3 Measure and integration (28-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Manifolds and cell complexes (57-XX) 3 Geophysics (86-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Information and communication theory, circuits (94-XX) 2 Field theory and polynomials (12-XX) 2 Ordinary differential equations (34-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Algebraic topology (55-XX) 2 Mechanics of deformable solids (74-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Potential theory (31-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