Calculus of Variations and Geometric Measure Theory

G. Carron - I. Mondello - D. Tewodrose

Kato meets Bakry-Émery

created by tewodrose on 15 May 2023



Inserted: 15 may 2023

Year: 2023

ArXiv: 2305.07428 PDF


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.