Selected problems from minkowski geometry [Elektronische Ressource] / vorgelegt von Nico Düvelmeyer

Selected ProblemsfromMinkowski Geometryvon der Fakultat fur Mathematik¨ ¨der Technischen Universitat Chemnitz genehmigte¨DISSERTATIONzur Erlangung des akademischen GradesDoctor rerum naturalium(Dr. rer. nat.)¨TECHNISCHE UNIVERSITAT CHEMNITZFakultat fur Mathematik¨ ¨vorgelegt von Dipl.-Math. Nico Duvelmeyer¨geb. am 30. Mai 1979 in Greiz eingereicht am 8. Juni 2006gefo¨rdert durch ein Stipendium der Studienstiftung des deutschen Volkes (4/2003 bis 3/2005)Gutachter: Prof. Dr. H. Martini (Betreuer, TU Chemnitz)Prof. Dr. K. J. Swanepoel (UNISA, Pretoria, South Africa)Prof. Dr. E. Hertel (Friedrichchiller-Universit a¨t Jena)Tag der Verteidigung: 9. November 2006Verfug¨ bar im MONARCH der TU Chemnitz: http://archiv.tu-chemnitz.de/pub/2006/0196PrefaceThe results of this dissertation refer to the geometry of Minkowski spaces, i.e., of finite dimensionalnormed linear spaces. Also in view of very recent developments, this field can be located at theintersectionofFinslerGeometry,BanachSpaceTheory,andConvexGeometry,butitisalsocloselyrelated to Distance Geometry and Abstract Convexity. Moreover, the main part of the obtainedresults belongs to the Discrete Geometry of normed planes, where the use of numerical methodsis new in this field. Having chosen such an approach, we follow the modern trend that numericalcomputations are based on exact arithmetics.