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PreprintarXiv licencearXiv

A proof of the Ashbaugh--Benguria conjecture for reciprocal sums of Neumann eigenvalues

  • Yixin He
  • Yanyang Li
  • Quanyu Tang
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Abstract

We prove the Ashbaugh--Benguria conjecture for bounded domains with Lipschitz boundary in ℝm. More precisely, among all bounded Lipschitz domains of fixed volume, the ball minimizes the sum of the reciprocals of the first m nonzero Neumann eigenvalues. Equality is attained precisely by balls.

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Cite

BibTeXRIS
BibTeX
@misc{he2026proof,
  title = {{A proof of the Ashbaugh--Benguria conjecture for reciprocal sums of Neumann eigenvalues}},
  author = {Yixin He and Yanyang Li and Quanyu Tang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.08271},
  eprint = {2606.08271},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.08271},
}
RIS
TY  - UNPB
TI  - A proof of the Ashbaugh--Benguria conjecture for reciprocal sums of Neumann eigenvalues
AU  - Yixin He
AU  - Yanyang Li
AU  - Quanyu Tang
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2606.08271
UR  - https://arxiv.org/abs/2606.08271
AB  - We prove the Ashbaugh--Benguria conjecture for bounded domains with Lipschitz boundary in ℝ^m. More precisely, among all bounded Lipschitz domains of fixed volume, the ball minimizes the sum of the reciprocals of the first m nonzero Neumann eigenvalues. Equality is attained precisely by balls.
ER  -