Improvements of upper curvature bounds

Lytchak, Alexander; Stadler, Stephan

doi:10.1090/tran/8123

Improvements of upper curvature bounds
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by Alexander Lytchak and Stephan Stadler PDF

Trans. Amer. Math. Soc. 373 (2020), 7153-7166 Request permission

Abstract:

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.

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