Monotonicity of harmonic functions on $3$-manifolds with an asymptotically flat end

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.

article composed in July 2025 for a special issue of Acta Mathematica Sinica, English Series