IMPROVEMENTS OF UPPER CURVATURE BOUNDS

被引：9

作者：

Lytchak, Alexander ^{[1
]}

Stadler, Stephan ^{[2
]}

机构：

[1] Univ Cologne, Mathemat Inst, Weyertal 86-90, D-50931 Cologne, Germany

[2] Univ Munich, Mathemat Inst, Theresienstr 39, D-80333 Munich, Germany

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2020年 / 373卷 / 10期

关键词：

Non-positive curvature; conformal change; minimal disc; harmonic maps; GRADIENT FLOWS; HARMONIC MAPS; RIEMANNIAN POLYHEDRA; CONVEX-FUNCTIONS; LOCAL-STRUCTURE; SPACES;

D O I：

10.1090/tran/8123

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that upper curvature bounds in the sense of Alexandrov can be improved locally by using appropriate conformal changes. As a new technical tool we derive a generalization to metric spaces and semi-convex functions of the classical differential geometric property that compositions of harmonic maps with convex functions are subharmonic.

引用

页码：7153 / 7166

页数：14

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