The rigidity statement in the Horowitz-Myers conjecture

2025/04/23 by Brendle, S., Hung, P. K. · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.16812

Abstract

In this paper, we give an alternative proof of the Horowitz-Myers conjecture in dimension 3 ≤ N ≤ 7. Moreover, we show that a metric that achieves equality in the Horowitz-Myers conjecture is locally isometric to a Horowitz-Myers metric.

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• Scalar curvature rigidity for products of spheres and tori
• On the geometry and uniqueness of asymptotically locally hyperbolic static vacuum black holes

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