Can I read Monotonicity and rigidity of the W-entropy on RCD(0, N) spaces on EtoBox?

Monotonicity and rigidity of the W-entropy on RCD(0, N) spaces by Kuwada, Kazumasa; Li, Xiang-Dong is a scholarly article available to read on EtoBox.

What is Monotonicity and rigidity of the W-entropy on RCD(0, N) spaces about?

By means of a space-time Wasserstein control, we show the monotonicity of the W-entropy functional in time along heat flows on possibly singular metric measure spaces with non-negative Ricci curvature and a finite upper bound of dimension in an appropriate sense. The associated rigidity result on the rate of dissipation of the W-entropy is also proved. These extend known results even on weighted Riemannian manifolds in some respects. In addition, we reveal that some singular spaces will exhibit the rigidity models while only the Euclidean space does in the class of smooth weighted Riemannian manifolds.

Author

Kuwada, Kazumasa; Li, Xiang-Dong

Published

2018

Language

EN