Positive mass theorems for manifolds with ALH toroidal ends
Differential Geometry
2026-02-10 v1 General Relativity and Quantum Cosmology
Abstract
In work with P. Chru\'sciel, L. Nguyen and T.-T. Paetz [8], a positive mass theorem was obtained for asymptotically locally hyperbolic manifolds with boundary, having a toroidal end. The proof made use of properties of marginally outer trapped surfaces (MOTS). Here we present some new PMT results for such manifolds, but without boundary, which allow for other more general ends. The proofs, while still MOTS-based, involve a more elaborate technique (related to -bubbles) introduced in work of D. A. Lee, M. Lesourd, and R. Unger [20] for manifolds with an asymptotically flat end, and further developed in [23] for manifolds with an asymptotically hyperbolic end.
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Cite
@article{arxiv.2602.08789,
title = {Positive mass theorems for manifolds with ALH toroidal ends},
author = {Gregory J. Galloway and Tin-Yau Tsang},
journal= {arXiv preprint arXiv:2602.08789},
year = {2026}
}
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11 pages