The Volume Entropy of a Riemannian Metric Evolving by the Ricci Flow on a Manifold of Dimension 3 or Above

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111587In this paper it is proven that the volume entropy of a riemannian metric evolving by the Ricci flow, if does not collapse, nondecreases. Therefore, it provides a sufficient condition for a solution to collapse. Then, for the limit solutions of type I or III, the limit entropy is the limit of the entropy as $t$ approaches the singular (finite or not) time.5 pagesDifferential GeometryAnalysis of PDEs58J35; 37B40The Volume Entropy of a Riemannian Metric Evolving by the Ricci Flow on a Manifold of Dimension 3 or Abovetext