Non-existence of Poincaré-Einstein manifolds with prescribed conformal infinity

DOI10.1007/s00039-017-0414-yzbMath1379.53058OpenAlexW2717008538MaRDI QIDQ2400826

Matthew J. Gursky, Qing Han

Publication date: 30 August 2017

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00039-017-0414-y

zbMATH Keywords

conformal infinityPoincaré-Einstein manifoldYamabe functional

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Rigidity results (53C24) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (13)

On conformally compact Einstein manifolds ⋮ Scalar flat compactifications of Poincaré-Einstein manifolds and applications ⋮ Comparison Between Conformal Invariants for Conformally Compact Einstein Metrics: Some Counter-Example from the Metrics Developed by Pedersen ⋮ Escobar-Yamabe compactifications for Poincaré-Einstein manifolds and rigidity theorems ⋮ Comparison theorems for GJMS operators ⋮ A remark on the rigidity of Poincaré-Einstein manifolds ⋮ Finite boundary regularity for conformally compact Einstein manifolds of dimension 4 ⋮ The asymptotically self-similar regime for the Einstein vacuum equations ⋮ A local existence result for Poincaré-Einstein metrics ⋮ An Obata-type theorem on compact Einstein manifolds with boundary ⋮ An invariant related to the existence of conformally compact Einstein fillings ⋮ On a sharp inequality relating Yamabe invariants on a Poincare-Einstein manifold ⋮ On uniqueness and existence of conformally compact Einstein metrics with homogeneous conformal infinity

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