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PreprintCC BY 4.0arXiv

Sharp lower bound of the first eigenvalue of the p-Laplacian under integral Ricci curvature

  • Shoo Seto
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Abstract

We prove a sharp Zhong-Yang type lower bound for the first nonzero eigenvalue of the p-Laplacian on closed manifolds with small integral Ricci curvature for p ≥ 2. The proof combines a global elliptic estimate obtained by Sobolev truncation with strict perturbations of one-dimensional comparison profiles.

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Cite

BibTeXRIS
BibTeX
@misc{seto2026sharp,
  title = {{Sharp lower bound of the first eigenvalue of the $p$-Laplacian under integral Ricci curvature}},
  author = {Shoo Seto},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12852},
  eprint = {2610.12852},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12852},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Sharp lower bound of the first eigenvalue of the p-Laplacian under integral Ricci curvature
AU  - Shoo Seto
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.12852
UR  - https://arxiv.org/abs/2610.12852
AB  - We prove a sharp Zhong-Yang type lower bound for the first nonzero eigenvalue of the p-Laplacian on closed manifolds with small integral Ricci curvature for p ≥ 2. The proof combines a global elliptic estimate obtained by Sobolev truncation with strict perturbations of one-dimensional comparison profiles.
ER  -