Year: 2026
Type: preprint
Abstract: We study positive mass and related Brown--York type inequalities for three-dimensional manifolds modeled on a static space with flat toroidal slices. Using inverse mean curvature flow, we first derive an inequality relating the asymptotic geometry at infinity to the size of an interior singularity. This inequality admits a natural interpretation as a positive mass type theorem. We then combine this global inequality with a Shi--Tam type construction to obtain a Brown--York type inequality for boundaries isometric to flat tori. In contrast to the Schwarzschild setting, our argument does not extend directly to general boundary surfaces, and we identify several obstructions to such a generalization. Finally, we discuss examples illustrating the relationship between negative mass, the strength of interior singularities, and the topology of the interior.
Source: arXiv (Cornell University)
Author: Wang, Zhixin
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214215849