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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{he2026qualitative,
  title = {{New Qualitative and Quantitative Estimates for Neumann Eigenvalues toward Pólya's Conjecture}},
  author = {Xiang He and Renjin Jiang and Fanghua Lin and Zuoqin Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19455},
  eprint = {2610.19455},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19455},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - New Qualitative and Quantitative Estimates for Neumann Eigenvalues toward Pólya's Conjecture
AU  - Xiang He
AU  - Renjin Jiang
AU  - Fanghua Lin
AU  - Zuoqin Wang
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19455
UR  - https://arxiv.org/abs/2610.19455
AB  - 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.
ER  -