Several isoperimetric inequalities of Dirichlet and Neumann eigenvalues of the Witten Laplacian

In this paper, by mainly using the rearrangement technique and suitably constructing trial functions, under the constraint of fixed weighted volume, we successfully obtain several isoperimetric inequalities for the first and the second Dirichlet eigenvalues, the first non-zero Neumann eigenvalue of...

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Bibliographic Details
Published inJournal of spectral theory Vol. 15; no. 3; pp. 1241 - 1277
Main Authors Chen, Ruifeng, Mao, Jing
Format Journal Article
LanguageEnglish
Published 01.01.2025
Online AccessGet full text
ISSN1664-039X
1664-0403
DOI10.4171/jst/564

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Summary:In this paper, by mainly using the rearrangement technique and suitably constructing trial functions, under the constraint of fixed weighted volume, we successfully obtain several isoperimetric inequalities for the first and the second Dirichlet eigenvalues, the first non-zero Neumann eigenvalue of the Witten Laplacian on bounded domains in space forms. These spectral isoperimetric inequalities extend the classical ones (i.e., the Faber–Krahn inequality, the Hong–Krahn–Szegő inequality, and the Szegő–Weinberger inequality) of the Laplacian.
ISSN:1664-039X
1664-0403
DOI:10.4171/jst/564