Geometric and spectral estimates based on spectral Ricci curvature assumptions-Reference-Cited by-同舟云学术

Geometric and spectral estimates based on spectral Ricci curvature assumptions

Published:2020-08-05 Issue:772 Volume:2021 Page:121-145
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Carron Gilles¹,Rose Christian²

Affiliation:

1. Université de Nantes , Département de Mathématiques , 2 rue de la Houssinière, BP 92208,44322 Nantes cedex 03 , France

2. Max Planck Institute for Mathematics in the Sciences , Inselstraße 22, 04103 Leipzig , Germany

Abstract

AbstractWe obtain a Bonnet–Myers theorem under a spectral condition: a closed Riemannian(Mn,g)

{(M^{n},g)}

manifold for which the lowest eigenvalue of the Ricci tensor ρ is such that the Schrödinger operatorΔ+(n-2)⁢ρ

{\Delta+(n-2)\rho}

is positive has finite fundamental group. Further, as a continuation of our earlier results, we obtain isoperimetric inequalities from Kato-type conditions on the Ricci curvature. We also obtain the Kato condition for the Ricci curvature under purely geometric assumptions.

Funder

Agence Nationale de la Recherche

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2020-0026/pdf

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