Results and Problems from Minkowski Geometry
主 题: Results and Problems from Minkowski Geometry
报告人: Professor Dr Horst Martini (TU Chemnitz, Germany)
时 间: 2014-11-12 14:00-15:00
地 点: 理科一号楼1479（主持人：宗传明）
Minkowski Geometry - the geometry of finite dimensional real Banach spaces - can be considered as an extensionb of Classical Convexity and a specification of Finsler Geometry. It goes back to H. Minkowski (ca.1900), and over the 20th century it was developed mainly in analytical directions, yielding finally a respective monograph of A. C. Thompson (1996). Recently various other (more discrete and applied) research fields contributed, since Minkowski spaces are also attractive for those disciplines. In the present talk an overview is given about recent research results in this spirit. The partial fields under discussion are: Convexity in Minkowski spaces (e.g., geometry of reduced bodies), Discrete and Computational Geometry (Fermat-Torricelli problem, universal covers), Curve theory in Minkowski planes (e.g., the geometry of Cassini curves), and Elementary Geometry there (geometry of Minkowskian triangles and circles). We also present an interesting collection of open research problems.