Monotonicity of harmonic functions on $3$-manifolds with an asymptotically flat end
Differential Geometry
2025-12-22 v1
Abstract
We derive monotone properties of positive harmonic functions on three dimensional manifolds with nonnegative scalar curvature, with an asymptotically flat end. Rigidity characterization of spatial Schwarzschild manifolds with two ends is also given.
Keywords
Cite
@article{arxiv.2512.17222,
title = {Monotonicity of harmonic functions on $3$-manifolds with an asymptotically flat end},
author = {Pengzi Miao},
journal= {arXiv preprint arXiv:2512.17222},
year = {2025}
}
Comments
article composed in July 2025 for a special issue of Acta Mathematica Sinica, English Series