Payne-P\'olya-Weinberger inequalities on closed Riemannian manifolds

Mehdi Eddaoudi

Payne-P\'olya-Weinberger inequalities on closed Riemannian manifolds

Spectral Theory 2025-03-27 v1 Mathematical Physics Differential Geometry math.MP

Authors: Mehdi Eddaoudi

Abstract

Payne-P\'olya-Weinberger inequalities are known to be exclusive to bounded Euclidean domains with Dirichlet boundary condition. In this paper, we discuss the corresponding inequalities on Riemannian manifolds of dimension $n \geq3$ , and we prove explicit bounds in terms of geometric quantities such as scalar curvature, Yamabe constant, isoperimetric constant and conformal volume.

Keywords

Payne-P\'olya-Weinberger inequality Riemannian manifold scalar curvature Yamabe constant isoperimetric constant

Cite

@article{arxiv.2503.20181,
  title  = {Payne-P\'olya-Weinberger inequalities on closed Riemannian manifolds},
  author = {Mehdi Eddaoudi},
  journal= {arXiv preprint arXiv:2503.20181},
  year   = {2025}
}

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