Integral Ricci curvature and the mass gap of Dirichlet Laplacians on domains
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...
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| Veröffentlicht in: | Mathematische Nachrichten 2023-08, Vol.296 (8), p.3559-3578 |
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| creator | Ramos Olivé, Xavier Rose, Christian Wang, Lili Wei, Guofang |
| description | 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 Lp$L^p$‐Ricci curvature assumptions, p>n/2$p>n/2$. 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. |
| doi_str_mv | 10.1002/mana.202100523 |
| format | Article |
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| subjects | Curvature Dirichlet problem eigenvalue estimate Eigenvalues integral Ricci curvature mass gap spectral gap |
| title | Integral Ricci curvature and the mass gap of Dirichlet Laplacians on domains |
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