Geometric and spectral estimates based on spectral Ricci curvature assumptions

Gilles Carron (1) , Rose Christian, (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 Chemnitz University of Technology / Technische Universität Chemnitz

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 Schr\"odinger 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

Mots clés: Sobolev inequality; isoperimetric inequality.

Domaines: Géométrie différentielle [math.DG]

Gilles Carron, Rose Christian,. Geometric and spectral estimates based on spectral Ricci curvature assumptions. Journal für die reine und angewandte Mathematik, 2020. ⟨hal-01859318⟩