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Paper detail

Rigidity of a trace estimate for Steklov eigenvalues

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.

preprint2020arXivOpen access
Yongjie ShiChengjie Yu
math.DG
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Yongjie ShiChengjie Yu

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