An invariant related to the existence of conformally compact Einstein fillings

2018/01/13 by Gursky, Matthew J., Han, Qing, Stolz, Stephan · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.04474

Abstract

We define an invariant for compact spin manifolds X of dimension 4k equipped with a metric h of positive Yamabe invariant on its boundary. The vanishing of this invariant is a necessary condition for the conformal class of h to be the conformal infinity of a conformally compact Einstein metric on X.

Cited by

• On the Poincaré-Einstein manifolds with cylindrical conformal infinity

Related

• On the structure of conformally compact Einstein metrics
• On compactness conformally compact Einstein manifolds and uniqueness of Graham-Lee metrics, III
• Boundary Curvature Scalars on Conformally Compact Manifolds
• Einstein metrics with prescribed conformal infinity on 4-manifolds
• Compactness of conformally compact Einstein manifolds in dimension 4