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

Mehdi Eddaoudi

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arXiv · 2503.20181

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

Mehdi Eddaoudi

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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.

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BibTeX RIS

Mehdi Eddaoudi. 2025-03-26. Payne-P\'olya-Weinberger inequalities on closed Riemannian manifolds. https://arxiv.org/abs/2503.20181

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