Orbifold compactness for spaces of Riemannian metrics and applications

2003/12/04 by Michael T. Anderson, Anderson, Michael T.
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.math/0312111

28pp. Exposition improved, references added

openalex publication_date 2003/12/04 · arxiv created 2004/01/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such compactness for spaces of Bach-flat (for example half-conformally flat) metrics on 4-manifolds, and related results for metrics which are critical points of other natural Riemannian functionals on the space of metrics.

Related

• Moduli spaces of flat Riemannian metrics on orbifolds
• Orbifold regularity of weak Kahler-Einstein metrics
• Compactness of conformally compact Einstein manifolds in dimension 4
• On the structure of conformally compact Einstein metrics
• On compactness conformally compact Einstein manifolds and uniqueness of Graham-Lee metrics, III