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

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  • Xavier Ramos Olivé
  • Christian Rose
  • Lili Wang
  • Guofang Wei

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 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.

Suggested Citation

  • Xavier Ramos Olivé & Christian Rose & Lili Wang & Guofang Wei, 2023. "Integral Ricci curvature and the mass gap of Dirichlet Laplacians on domains," Mathematische Nachrichten, Wiley Blackwell, vol. 296(8), pages 3559-3578, August.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:8:p:3559-3578
    DOI: 10.1002/mana.202100523
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