Published Paper

Inserted: 5 mar 2025
Last Updated: 25 aug 2025

Journal: manuscripta math.
Year: 2025
Doi: 10.1007/s00229-025-01663-6

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.