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Geometric and spectral estimates based on spectral Ricci curvature assumptions
Journal für die reine und angewandte Mathematik ( IF 1.5 ) Pub Date : 2021-03-01 , DOI: 10.1515/crelle-2020-0026
Gilles Carron 1 , Christian Rose 2
Affiliation  

We obtain a Bonnet–Myers theorem under a spectral condition: a closed Riemannian ( M n , g ) {(M^{n},g)} manifold for which the lowest eigenvalue of the Ricci tensor ρ is such that the Schrödinger operator Δ + ( 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.

中文翻译:

基于频谱Ricci曲率假设的几何和频谱估计

我们得到一个在频谱条件下的Bonnet-Myers定理:一个封闭的黎曼(M n,g){(M ^ {n},g)}流形,其Ricci张量ρ的最低特征值使得Schrödinger算子Δ +(n-2)⁢ρ{\ Delta +(n-2)\ rho}是正的,具有有限的基群。此外,作为我们先前结果的延续,我们从Ricci曲率的Kato型条件中获得了等距不等式。我们还可以在纯几何假设下获得Ricci曲率的Kato条件。
更新日期:2021-03-16
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