Scalar curvature deformation and mass rigidity for ALH manifolds with boundary

2021/08/29 by Lan-Hsuan Huang, Hyun Chul Jang, Huang, Lan-Hsuan +1 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2108.12887

openalex publication_date 2021/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study scalar curvature deformation for asymptotically locally hyperbolic (ALH) manifolds with nonempty compact boundary. We show that the scalar curvature map is locally surjective among either (1) the space of metrics that coincide exponentially toward the boundary, or (2) the space of metrics with arbitrarily prescribed nearby Bartnik boundary data. Using those results, we characterize the ALH manifolds that minimize the Wang-Chruściel-Herzlich mass integrals in great generality and establish the rigidity of the positive mass theorems.

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