Hopf type theorem for surfaces of constant weighted mean curvature in Riemannian manifolds

Jiaming Chen; Shanze Gao

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arXiv · 2608.23036

Hopf type theorem for surfaces of constant weighted mean curvature in Riemannian manifolds

Jiaming Chen·Shanze Gao

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Abstract

We consider compact immersed surfaces of genus zero in a three-dimensional smooth metric measure space $(M^3,g,e^{-f}\mathrm{d}V_{g})$. We introduce a new weighted mean curvature and prove that any such surface whose weighted mean curvature is constant must be totally umbilical, provided that a condition relating the Ricci curvature of $M$ and the weight function $f$ is satisfied. We also give an application of this result to the uniqueness of the dual Christoffel-Minkowski problem.

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BibTeX RIS

Jiaming Chen, Shanze Gao. 2026-08-24. Hopf type theorem for surfaces of constant weighted mean curvature in Riemannian manifolds. https://arxiv.org/abs/2608.23036

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