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arXiv · 2610.19455

New Qualitative and Quantitative Estimates for Neumann Eigenvalues toward Pólya's Conjecture

Xiang He·Renjin Jiang·Fanghua Lin·Zuoqin Wang
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Abstract

We introduce the Enhanced Neumann Pólya inequality, which is stronger than Pólya's conjecture, and verify it for many classes of domains, including strip-tiling domains, Euclidean balls, thin product domains, and certain higher-dimensional tiling domains. We develop a geometric removal approach for the Enhanced Neumann Pólya inequality. In particular, our results provide new classes of domains satisfying the Neumann part of Pólya's conjecture.

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Xiang He, Renjin Jiang, Fanghua Lin, Zuoqin Wang. 2026-10-14. New Qualitative and Quantitative Estimates for Neumann Eigenvalues toward Pólya's Conjecture. https://arxiv.org/abs/2610.19455

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