Brock-type isoperimetric inequality for Steklov eigenvalues of the Witten-Laplacian
Analysis of PDEs
2024-04-12 v1 Differential Geometry
Abstract
In this paper, by imposing suitable assumptions on the weighted function, (under the constraint of fixed weighted volume) a Brock-type isoperimetric inequality for Steklov-type eigenvalues of the Witten-Laplacian on bounded domains in a Euclidean space or a hyperbolic space has been proven. This conclusion is actually an interesting extension of F. Brock's classical result about the isoperimetric inequality for Steklov eigenvalues of the Laplacian given in the influential paper [Z. Angew. Math. Mech. 81 (2001) 69-71]. Besides, a related open problem has also been proposed in this paper.
Cite
@article{arxiv.2404.07412,
title = {Brock-type isoperimetric inequality for Steklov eigenvalues of the Witten-Laplacian},
author = {Jing Mao and Shijie Zhang},
journal= {arXiv preprint arXiv:2404.07412},
year = {2024}
}
Comments
18 pages. Comments are welcome. arXiv admin note: text overlap with arXiv:2403.08070