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arXiv · 2512.19329

An overdetermined problem related to the p-Laplacian on Riemannian manifolds

Guangyue Huang·Chunlei Luo·Hongru Song
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Abstract

In this paper, we study the overdetermined problem for the p-Laplacian equation on a compact Riemannian manifold with positive Ricci curvature. By introducing a new P-function which is related to the first nonzero eigenvalue for p-Laplacian, we obtain some integral identities. As their applications, the Heintze-Karcher type inequality and the Soap Bubble Theorem have been achieved.

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Guangyue Huang, Chunlei Luo, Hongru Song. 2025-12-22. An overdetermined problem related to the p-Laplacian on Riemannian manifolds. https://arxiv.org/abs/2512.19329

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