paper

Perelman's entropy and heat kernel bounds on RCD spaces

arXiv:2503.03017

Abstract

We study Perelman's W-entropy functional on finite-dimensional RCD spaces, a synthetic generalization of spaces with Bakry-Émery 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.

Perelman's entropy and heat kernel bounds on RCD spaces · wovepaper