Unique continuation results for Ricci curvature and applications

TL;DR

This paper establishes unique continuation properties for metrics with prescribed Ricci curvature on compact and conformally compact manifolds, and explores isometry extension and invariance of constraint equations in geometric analysis.

Contribution

It proves new unique continuation results for Ricci curvature metrics and demonstrates isometry extension properties in conformally compact Einstein manifolds.

Findings

Unique continuation results for Ricci curvature metrics.

Isometry groups at conformal infinity extend into the bulk.

Relations between isometry extension and Gauss-Codazzi invariance.

Abstract

Unique continuation results are proved for metrics with prescribed Ricci curvature in the setting of bounded metrics on compact manifolds with boundary, and in the setting of complete, conformally compact metrics. Related to this issue, an isometry extension property is proved: continuous groups of isometries at conformal infinity extend into the bulk of any complete conformally compact Einstein metric. Relations of this property with the invariance of the Gauss-Codazzi constraint equations under deformations are also discussed.