Rigidity of a trace estimate for Steklov eigenvalues
Differential Geometry
2020-01-22 v2
Abstract
In this short note, we show the rigidity of a trace estimate for Steklov eigenvalues with respect to functions in our previous work (Trace and inverse trace of Steklov eigenvalues. J. Differential Equations 261 (2016), no. 3, 2026--2040.). Namely, we show that equality of the estimate holds if and only if the manifold is a direct product of a round ball and a closed manifold. The key ingredient in the proof is a decomposition theorem for flat and totally geodesic Riemannian submersions which may be of independent interests.
Keywords
Cite
@article{arxiv.1912.12785,
title = {Rigidity of a trace estimate for Steklov eigenvalues},
author = {Yongjie Shi and Chengjie Yu},
journal= {arXiv preprint arXiv:1912.12785},
year = {2020}
}
Comments
A mistake was fixed