Perelman's entropy and heat kernel bounds on RCD spaces
Differential Geometry
2025-03-06 v1
Abstract
We study Perelman's W-entropy functional on finite-dimensional RCD spaces, a synthetic generalization of spaces with Bakry-\'{E}mery Ricci curvature bounded from below. We rigorously justify the formula for the time derivative of the W-entropy and derive its monotonicity and rigidity properties. Additionally, we establish bounds for solutions of the heat equation, which are of independent interest.
Keywords
Cite
@article{arxiv.2503.03017,
title = {Perelman's entropy and heat kernel bounds on RCD spaces},
author = {Camillo Brena},
journal= {arXiv preprint arXiv:2503.03017},
year = {2025}
}