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arXiv · 2109.11181

Integral Ricci curvature and the mass gap of Dirichlet Laplacians on domains

Xavier Ramos Olivé·Christian Rose·Lili Wang·Guofang Wei
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Abstract

We obtain a fundamental gap estimate for classes of bounded domains with quantitative control on the boundary in a complete manifold with integral bounds on the negative part of the Ricci curvature. This extends the result of \cite{Oden-Sung-Wang99} to $L^p$-Ricci curvature assumptions, $p>n/2$. To achieve our result, it is shown that the domains under consideration are John domains, what enables us to obtain an estimate on the first nonzero Neumann eigenvalue, which is of independent interest.

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Xavier Ramos Olivé, Christian Rose, Lili Wang, Guofang Wei. 2021-09-23. Integral Ricci curvature and the mass gap of Dirichlet Laplacians on domains. https://arxiv.org/abs/2109.11181

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