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This paper generalizes D. Burago and S. Ivanov's work on filling volumeminimality and boundary rigidity of almost real hyperbolic metrics. We showthat regions with metrics close to a negatively curved symmetric metric arestrict minimal fillings and hence boundary rigid. This includes perturbationsof complex, quaternionic and Cayley hyperbolic metrics.

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