Boundary regularity for asymptotically hyperbolic metrics with smooth Weyl curvature

2018/01/14 by Xiaoshang Jin
Mathematics · #Advanced Harmonic Analysis Research #Boundary (topology) #Boundary value problem #Conformal map #Curvature #Einstein #Geometric Analysis and Curvature Flows #Mean curvature #Metric (unit) #Nonlinear Partial Differential Equations #math.DG

paper · pdf · doi:10.2140/pjm.2019.301.467

published as Pacific J. Math. 301 (2019) 467-487 · 24 pages

arxiv created 2018/01/14 · openalex created_date 2018/01/26 · openalex publication_date 2019/10/24 · arxiv updated 2019/10/30 · openalex updated_date 2026/08/05

Abstract

In this paper, we study the regularity of asymptotically hyperbolic metrics with Einstein condition near boundary and Weyl curvature smooth enough in arbitrary dimension. Following Michael Anderson's method, we show that C^m,α conformally compact Riemannian metrics with Einstein equation vanishing to finite order near boundary have conformal compactifications that are C^m+2,α up to the boundary when Weyl curvature is in C^m,α and the boundary metric is in C^m+2,α where m≥ 3.

Citations

• Some regularity theorems in riemannian geometry
• Multiple Integrals in the Calculus of Variations
• Einstein metrics with prescribed conformal infinity on the ball