Geometric and spectral estimates based on spectral Ricci curvature assumptions

2018/08/21 by Gilles Carron, Christian Rose, Carron, Gilles +1 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.1808.06965

openalex publication_date 2018/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain a Bonnet-Myers theorem under a spectral condition: a closed Riemannian manifold (Mⁿ,g) for which the lowest eigenvalue of the Ricci tensor ρ is such that the Schrödinger operator (n-2)Δ+ ρ is positive has finite fundamental group. As a continuation of our earlier results, we obtain isoperimetric inequalities from a Kato condition on the Ricci curvature. Furthermore, we obtain the Kato condition for the Ricci curvature under purely geometric assumptions.

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