An isoperimetric inequality for lower order Neumann eigenvalues in Gauss space

Yi Gao; Kui Wang

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arXiv · 2503.15813

An isoperimetric inequality for lower order Neumann eigenvalues in Gauss space

Yi Gao·Kui Wang

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Abstract

We prove a sharp isoperimetric inequality for the harmonic mean of the first $m-1$ nonzero Neumann eigenvalues for bounded Lipschitz domains symmetric about the origin in Gauss space. Our result generalizes the Szeg\"o-Weinberger type inequality in Gauss space, as proved in [8, Theorem 4.1].

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Yi Gao, Kui Wang. 2025-03-20. An isoperimetric inequality for lower order Neumann eigenvalues in Gauss space. https://arxiv.org/abs/2503.15813

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