Low regularity Poincaré–Einstein metrics
Copyright policy )Low regularity Poincaré–Einstein metrics
We prove the existence of a C 1 , 1 C^{1,1} conformally compact Einstein metric on the ball that has asymptotic sectional curvature decay to − 1 -1 plus terms of order e − 2 r e^{-2r} where r r is the distance from any fixed compact set. This metric has no C 2 C^2 conformal compactification.
- Antioch University Santa Barbara United States
- University of Washington United States
- University of Mary United States
Mathematics - Differential Geometry, regularity, conformal compactification, 53C25, 58J32, Smoothness and regularity of solutions to PDEs, quadratic hyperbolic curvature decay, Boundary value problems for second-order elliptic systems, Einstein metric, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Degenerate elliptic equations, Special Riemannian manifolds (Einstein, Sasakian, etc.), Mathematics - Analysis of PDEs, Differential Geometry (math.DG), FOS: Mathematics, Analysis of PDEs (math.AP)
Mathematics - Differential Geometry, regularity, conformal compactification, 53C25, 58J32, Smoothness and regularity of solutions to PDEs, quadratic hyperbolic curvature decay, Boundary value problems for second-order elliptic systems, Einstein metric, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Degenerate elliptic equations, Special Riemannian manifolds (Einstein, Sasakian, etc.), Mathematics - Analysis of PDEs, Differential Geometry (math.DG), FOS: Mathematics, Analysis of PDEs (math.AP)
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