Volume Comparison of Conformally Compact Manifolds with Scalar Curvature R ≥ −n (n − 1)

Volume Comparison of Conformally Compact Manifolds with Scalar Curvature R ≥ −n (n − 1)

In this paper, we use the normalized Ricci–DeTurk flow to prove a stability result for strictly stable conformally compact Einstein manifolds. As an application, we show a local volume comparison of conformally compact manifolds with scalar curvature R  ≥ − n ( n − 1) and also the rigidity result wh...

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Veröffentlicht in:Annales Henri Poincaré 2016-04, Vol.17 (4), p.953-977
Hauptverfasser: Hu, Xue, Ji, Dandan, Shi, Yuguang
Format: Artikel
Sprache:eng
Schlagworte:
Classical and Quantum Gravitation
Curvature
Dynamical Systems and Ergodic Theory
Elementary Particles
Flow stability
Manifolds
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity Theory
Theoretical
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Zusammenfassung:In this paper, we use the normalized Ricci–DeTurk flow to prove a stability result for strictly stable conformally compact Einstein manifolds. As an application, we show a local volume comparison of conformally compact manifolds with scalar curvature R  ≥ − n ( n − 1) and also the rigidity result when certain relative volume is zero.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-015-0411-3