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Pré-Publication, Document De Travail Année : 2023

Kato meets Bakry-\'Emery

Résumé

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.

Dates et versions

hal-04297981 , version 1 (21-11-2023)

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Gilles Carron, Ilaria Mondello, David Tewodrose. Kato meets Bakry-\'Emery. 2023. ⟨hal-04297981⟩
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