2018/03/08 by Simon Raulot
Mathematics · #Compactification (mathematics) #Conformal map #Elementary proof #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Hyperbolic space #Invariant (physics) #Invariant manifold #Manifold (fluid mechanics) #Nonlinear Partial Differential Equations #Rigidity (electromagnetism) #Symmetric space #math.DG
paper · pdf · doi:10.1007/s11005-018-01146-8
arxiv created 2018/03/08 · openalex created_date 2018/03/29 · openalex publication_date 2018/12/18 · arxiv updated 2019/01/30 · openalex updated_date 2026/08/05
In this paper, we give an optimal inequality relating the relative Yamabe invariant of a certain compactification of a conformally compact Poin-caré-Einstein manifold with the Yamabe invariant of its boundary at infinity. As an application, we obtain an elementary proof of the rigidity of the hyper-bolic space as the only conformally compact Poincaré-Einstein manifold with the round sphere as its conformal infinity.