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arXiv · 2404.06719

Shannon's inequality on non-collapsing RCD spaces

Yu Kitabeppu
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Abstract

We prove the Shannon's inequality on non-collapsing $\mathsf{RCD}(0,N)$ spaces. In the proof, we use the characterization of the $\mathsf{EVI}_{0,N}$-gradient flow of the relative entropy and the infinitesimal behavior of the heat kernel. Also we have a cone rigidity result. As an application, we have the so-called uncertainty principle inequality on such spaces.

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Yu Kitabeppu. 2024-11-07. Shannon's inequality on non-collapsing RCD spaces. https://arxiv.org/abs/2404.06719

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