Non-existence of concave functions on certain metric spaces

Yin Jiang

Non-existence of concave functions on certain metric spaces

Metric Geometry 2021-08-17 v1 Differential Geometry

Authors: Yin Jiang

Abstract

In the paper \cite{yau1974convex}, Yau proved that: There is no non-trivial continuous concave function on a complete manifold with finite volume. We prove analogue theorems for several metric spaces, including Alexandrov spaces with curvature bounded below/above, $C^{\alpha}$ -H\"older Riemannian manifolds.

Keywords

concave function metric space alexandrov space curvature bound holder riemannian manifold nonexistence

Cite

@article{arxiv.2108.07038,
  title  = {Non-existence of concave functions on certain metric spaces},
  author = {Yin Jiang},
  journal= {arXiv preprint arXiv:2108.07038},
  year   = {2021}
}

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19pages

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