An overdetermined problem related to the p-Laplacian on Riemannian manifolds
Analysis of PDEs
2025-12-23 v1 Differential Geometry
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.
Cite
@article{arxiv.2512.19329,
title = {An overdetermined problem related to the p-Laplacian on Riemannian manifolds},
author = {Guangyue Huang and Chunlei Luo and Hongru Song},
journal= {arXiv preprint arXiv:2512.19329},
year = {2025}
}
Comments
9 pages