ℱK-convex functions on metric spaces

被引：0
|
作者：
Stephanie Alexander
Richard L. Bishop
机构：
[1] Department of Mathematics,
[2] University of Illinois,undefined
[3] Urbana,undefined
[4] IL 61801,undefined
[5] USA. e-mail: sba@math.uiuc.edu,undefined
[6] Department of Mathematics,undefined
[7] University of Illinois,undefined
[8] Urbana,undefined
[9] IL 61801,undefined
[10] USA. e-mail: bishop@math.uiuc.edu,undefined
来源：
manuscripta mathematica | 2003年 / 110卷
关键词：
Approximation Theorem; Lipschitz Extension;
D O I：
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中图分类号：
学科分类号：
摘要：
 By an ℱK-convex function on a length metric space, we mean one that satisfies fn ≥ −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.
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页码：115 / 133
页数：18
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