Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: physics
1
The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph