?<Emphasis Type="Italic">K</Emphasis>-convex functions on metric spaces |
| |
| Authors: | Stephanie Alexander Richard L Bishop |
| |
| Institution: | (1) Department of Mathematics, University of Illinois, Urbana, IL 61801, USA. e-mail: sba@math.uiuc.edu, US;(2) Department of Mathematics, University of Illinois, Urbana, IL 61801, USA. e-mail: bishop@math.uiuc.edu, US |
| |
| Abstract: | By an ℱK-convex function on a length metric space, we mean one that satisfies f
n
≥ −Kf on all unitspeed geodesics. We show that natural ℱK-convex (-concave) functions occur in abundance on metric spaces of curvature bounded above (below) by K in the sense of Alexandrov. We prove Lipschitz extension and approximation theorems for ℱK-convex functions on CAT(K) spaces.
Received: 10 May 2002
Mathematics Subject Classification (2000): 53C70, 52A41 |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
