English

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