Integral Ricci curvature and the mass gap of Dirichlet Laplacians on domains |
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| Authors: | Xavier Ramos Olivé Christian Rose Lili Wang Guofang Wei |
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| Institution: | 1. Department of Mathematical Sciences, Smith College, Northampton, Massachusetts, USA;2. Institute of Mathematics, University of Potsdam, Potsdam, Germany;3. College of Mathematics and Information, FJKLMAA, Fujian Normal University, Fuzhou, China;4. Department of Mathematics, University of California Santa Barbara, Santa Barbara, California, USA |
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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 Oden, Sung, and Wang Trans. Amer. Math. Soc. 351 (1999), no. 9, 3533–3548] to -Ricci curvature assumptions, . 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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| Keywords: | eigenvalue estimate integral Ricci curvature mass gap spectral gap |
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