Shannon's inequality on non-collapsing RCD spaces

2024/04/10 by Yu Kitabeppu, Kitabeppu, Yu
Biochemistry, Genetics and Molecular Biology · Engineering · Immunology and Microbiology · #Dermatological and Skeletal Disorders #Elasticity and Material Modeling #FOS: Mathematics #Metric Geometry (math.MG) #Phagocytosis and Immune Regulation

paper · pdf · doi:10.48550/arxiv.2404.06719

openalex publication_date 2024/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the Shannon's inequality on non-collapsing RCD(0,N) spaces. In the proof, we use the characterization of the 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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