Mass Rigidity for Hyperbolic Manifolds

  • Lan-Hsuan HuangEmail author
  • Hyun Chul Jang
  • Daniel Martin


We prove the rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. Namely, if the mass equality \(p_0=\sqrt{p_1^2+\cdots + p_n^2}\) holds, then the manifold is isometric to hyperbolic space. The result was previously proven for spin manifolds (Andersson and Dahl in Ann Glob Anal Geom 16(1):1–2, 1998; Chruściel and Herzlich in Pac J Math 212(2):231–264, 2003; Min-Oo in Math Ann 285(4):527–539; 1989, Wang in J Differ Geom 57(2):273–299, 2001) or under special asymptotics (Andersson et al. in Ann. Henri Poincaré 9(1):1–33, 2008).



The project was initiated while the authors participated in the 2017 summer program on Geometry and Relativity at the Erwin Schrödinger Institute. We would like to express our sincere gratitude to the organizers Robert Beig, Piotr Chruściel, Michael Eichmair, Greg Galloway, Richard Schoen, Tim-Torben Paetz for their warm hospitality and the inspiring program. The project was partially supported by the NSF Career award DMS-1452477. L.-H. Huang was also supported by Simons Fellowship of the Simons Foundation and von Neumann Fellowship at the Institute for Advanced Study.


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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ConnecticutStorrsUSA
  2. 2.Department of MathematicsTrinity CollegeHartfordUSA

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