Fredholm operators and Einstein metrics on conformally compact manifolds

2006/01/01 by John M. Lee · 4 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.1090/memo/0864

openalex publication_date 2006/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/30

Abstract

The main result of this paper is the existence of asymptotically hyperbolic Einstein metrics with prescribed conformal infinity sufficiently close to that of a given asymptotically hyperbolic Einstein metric with nonpositive curvature. If the conformal infinities are sufficiently smooth, the resulting Einstein metrics have optimal Hlder regularity at the boundary. The proof is based on sharp Fredholm theorems for self-adjoint geometric linear elliptic operators on asymptotically hyperbolic manifolds.

Citations

• Differential equations on riemannian manifolds and their geometric applications
• The mass of an asymptotically flat manifold
• Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds

Cited by

• On non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics
• Unique continuation results for Ricci curvature and applications
• A SUB-PRODUCT CONSTRUCTION OF POINCARÉ–EINSTEIN METRICS
• John M. Lee [wikipedia]