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

TL;DR

This paper proves that regions with metrics close to negatively curved symmetric metrics are minimal fillings and boundary rigid, extending previous work to include perturbations of various hyperbolic metrics.

Contribution

It generalizes boundary rigidity and filling volume minimality results to metrics near negatively curved symmetric spaces, including complex, quaternionic, and Cayley hyperbolic metrics.

Findings

Regions close to negatively curved symmetric metrics are strict minimal fillings.

Such regions are boundary rigid.

Includes perturbations of complex, quaternionic, and Cayley hyperbolic metrics.

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.