Camillo Brena — Neckpinchhttps://neckpinch.com/authors/camillo-brena/New arXiv papers by Camillo Brena, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT Perelman's entropy and heat kernel bounds on RCD spaceshttps://neckpinch.com/papers/2503.03017/arxiv:2503.03017Tue, 04 Mar 2025 00:00:00 GMTCamillo Brena — 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 entropyHeat kernelWeak & singular flowsLimit spaces & RCDStability & uniqueness