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arXiv · 1912.12785

Rigidity of a trace estimate for Steklov eigenvalues

Yongjie Shi·Chengjie Yu
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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.

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Yongjie Shi, Chengjie Yu. 2019-12-30. Rigidity of a trace estimate for Steklov eigenvalues. https://arxiv.org/abs/1912.12785

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