scholarly journals Almost rigidity of the positive mass theorem for asymptotically hyperbolic manifolds with spherical symmetry

2017 ◽  
Vol 49 (9) ◽  
Author(s):  
Anna Sakovich ◽  
Christina Sormani
Keyword(s):  
Spherical Symmetry ◽  
Hyperbolic Manifolds ◽  
Positive Mass Theorem ◽  
Positive Mass ◽  
Asymptotically Hyperbolic Manifolds ◽  
Asymptotically Hyperbolic ◽  
Almost Rigidity

scholarly journals A positive mass theorem for asymptotically hyperbolic manifolds with inner boundary

2015 ◽  
Vol 26 (12) ◽  
pp. 1550101 ◽  
Author(s):  
Oussama Hijazi ◽  
Sebastián Montiel ◽  
Simon Raulot
Keyword(s):  
Riemannian Manifolds ◽  
Hyperbolic Manifolds ◽  
Positive Mass Theorem ◽  
Positive Mass ◽  
Asymptotically Hyperbolic Manifolds ◽  
Spin Manifolds ◽  
Asymptotically Hyperbolic

In this paper, we prove an optimal Positive Mass theorem for Asymptotically Hyperbolic spin manifolds with compact inner boundary. This improves a previous result of Chruściel and Herzlich [The mass of asymptotically hyperbolic Riemannian manifolds, Pacific J. Math. 212(2) (2003) 231–264].

scholarly journals The Jang Equation and the Positive Mass Theorem in the Asymptotically Hyperbolic Setting

2021 ◽  
Author(s):  
Anna Sakovich
Keyword(s):  
Initial Data ◽  
Spatial Dimension ◽  
Positive Mass Theorem ◽  
Positive Mass ◽  
Asymptotically Hyperbolic ◽  
Jang Equation

AbstractWe solve the Jang equation with respect to asymptotically hyperbolic “hyperboloidal” initial data. The results are applied to give a non-spinor proof of the positive mass theorem in the asymptotically hyperbolic setting. This work focuses on the case when the spatial dimension is equal to three.

scholarly journals Sharp Resolvent Estimates on Non-positively Curved Asymptotically Hyperbolic Manifolds

2020 ◽  
Author(s):  
Yiran Wang
Keyword(s):  
Energy Estimate ◽  
Weighted Sobolev Spaces ◽  
High Energy ◽  
Oscillatory Behavior ◽  
Hyperbolic Manifolds ◽  
Resolvent Estimates ◽  
Positive Sectional Curvature ◽  
Asymptotically Hyperbolic Manifolds ◽  
Asymptotically Hyperbolic ◽  
Positively Curved

Abstract We study the high energy estimate for the resolvent $R(\lambda )$ of the Laplacian on non-trapping asymptotically hyperbolic manifolds (AHMs). In the literature, estimates of $R(\lambda )$ on weighted Sobolev spaces of the order $O(|\lambda |^{N})$ were established for some $N> -1$, $|\lambda |$ large, and $\lambda \in{{\mathbb{C}}}$ in strips where $R(\lambda )$ is holomorphic. In this work, we prove the optimal bound $O(|\lambda |^{-1})$ under the non-positive sectional curvature assumption by taking into account the oscillatory behavior of the Schwartz kernel of the resolvent.

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