Symmetric orthogonality and non-expansive projections in metric spaces

Autor:	Kell, Martin
Rok vydání:	2016
Předmět:	Mathematics - Metric Geometry Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	In this paper known results of symmetric orthogonality, as introduced by G. Birkhoff, and non-expansive nearest point projections are extended from the linear to the metric setting. If the space has non-positive curvature in the sense Busemann then it is shown that those concepts are actually equivalent. In the end it is shown that every space having non-positive curvature in the sense of Busemann is a $CAT(0)$-space provided that its tangent cones are uniquely geodesic and their nearest point projections onto convex are non-expansive. Comment: 15 pages. Simplified presentation, removed Pedersen convexity, more direct proof of Theorem 19. Comments welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1604.01993 Zobrazit plný text záznamu View this record from Arxiv