Filling volume minimality and boundary rigidity of metrics close to a negatively curved symmetric metric

2022/01/23 by Yuping Ruan, Ruan, Yuping
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2201.09175

openalex publication_date 2022/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper generalizes D. Burago and S. Ivanov's work on filling volume minimality and boundary rigidity of almost real hyperbolic metrics. We show that regions with metrics close to a negatively curved symmetric metric are strict minimal fillings and hence boundary rigid. This includes perturbations of complex, quaternionic and Cayley hyperbolic metrics.

Related

• Volume comparison via boundary distances
• Rigidity for critical metrics of the volume functional
• Rigidity of Totally Geodesic Hypersurfaces in Negative Curvature
• Boundary rigidity of negatively-curved asymptotically hyperbolic\n surfaces
• Rigidity of manifolds with boundary under a lower Ricci curvature bound