Non-existence of concave functions on certain metric spaces

Yin Jiang

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arXiv · 2108.07038

Non-existence of concave functions on certain metric spaces

Yin Jiang

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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, $C^α$-Hölder Riemannian manifolds.

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BibTeX RIS

Yin Jiang. 2021-08-16. Non-existence of concave functions on certain metric spaces. https://arxiv.org/abs/2108.07038

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