Affiliation:
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
Abstract
AbstractWe 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.
Funder
National Science Foundation
Natural Science Foundation of Fujian Province
Cited by
3 articles.
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