Linear combinations of convex hypersurfaces in non-Euclidean geometry

被引：0
|
作者：
Kurt Leichtweiss
机构：
[1] Fachbereich Mathematik der Universitaet,
来源：
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry | 2012年 / 53卷 / 1期
关键词：
Linear combination of convex bodies; Radial map of the spherical resp. Weierstrass model; Distance convex bodies in hyperbolic space; Quasi support functions in spherical space; 52A55;
D O I：
10.1007/s13366-011-0080-4
中图分类号：
学科分类号：
摘要：
It is the aim of the paper to generalize the Minkowski addition, and more general, the Minkowski linear combination for a pair of convex bodies M1 and M2 in the euclidean n-space to non-Euclidean geometry. We succeed in the spherical case for arbitrary spherically convex bodies, whereas in the hyperbolic case the class of hyperbolically convex bodies has to be restricted in a suitable way. Practical computation of these operations for M1 and M2 is indicated after representation of their boundaries ∂M1 and ∂M2 with the help of certain support functions.
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页码：77 / 88
页数：11
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