Shannon's inequality on non-collapsing RCD spaces
Metric Geometry
2024-11-08 v2
Abstract
We prove the Shannon's inequality on non-collapsing spaces. In the proof, we use the characterization of the -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.
Cite
@article{arxiv.2404.06719,
title = {Shannon's inequality on non-collapsing RCD spaces},
author = {Yu Kitabeppu},
journal= {arXiv preprint arXiv:2404.06719},
year = {2024}
}