Kato meets Bakry-Émery

Gilles Carron, Ilaria Mondello, David Tewodrose

Research output: Working paperPreprint

1 Downloads (Pure)

Abstract

We prove that any complete Riemannian manifold with negative part of the Ricci curvature in a suitable Dynkin class is bi-Lipschitz equivalent to a finite-dimensional $\mathrm{RCD}$ space, by building upon the transformation rule of the Bakry-\'Emery condition under time change. We apply this result to show that our previous results on the limits of closed Riemannian manifolds satisfying a uniform Kato bound carry over to limits of complete manifolds. We also obtain a weak version of the Bishop-Gromov monotonicity formula for manifolds satisfying a strong Kato bound.
Original languageUndefined/Unknown
Publication statusPublished - 12 May 2023

Bibliographical note

18 pages, comments are welcome!

Cite this