Year: 2026
Type: preprint
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 surfaces in $\mathbb{R}^3$ satisfying $|x|^{2} H + 2\langle x,ν\rangle = c$.
Source: arXiv (Cornell University)
Authors: Chen, Jiaming, Gao, Shanze
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204186845