Some splitting and rigidity results for sub‐static spaces
Giulio Colombo, Allan Freitas, Luciano Mari, Marco Rigoli
Source abstract
Abstract In this paper, we study the rigidity problem for sub‐static systems with possibly nonempty boundary. First, we get local and global splitting theorems by assuming the existence of suitable compact minimal hypersurfaces, complementing recent results in the literature. Next, we prove some boundary integral inequalities that extend works by Chruściel and Boucher–Gibbons–Horowitz to nonvacuum spaces. Even in the vacuum static case, the inequalities improve on known ones. Finally, we consider the system arising from static solutions to the Einstein field equations coupled with a ‐model. The Liouville theorem we obtain allows for positively curved target manifolds, generalizing a result by Reiris.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.