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arXiv · 1808.06965

Geometric and spectral estimates based on spectral Ricci curvature assumptions

Gilles Carron·Christian Rose
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Abstract

We obtain a Bonnet-Myers theorem under a spectral condition: a closed Riemannian manifold $(M^n,g)$ for which the lowest eigenvalue of the Ricci tensor $\rho$ is such that the Schr\"odinger operator $(n-2)\Delta + \rho$ 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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Gilles Carron, Christian Rose. 2018-08-21. Geometric and spectral estimates based on spectral Ricci curvature assumptions. https://arxiv.org/abs/1808.06965

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