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

This paper generalizes D. Burago and S. Ivanov’s work (Duke Math J 162:1205–1248, 2013) 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.