Weighted manifolds satisfy a Riemannian Penrose inequality whose equality holds precisely for unique weighted static metrics with weighted minimal boundaries, via conformal equivalence to standard static metrics.
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Mass, Staticity, and a Riemannian Penrose Inequality for Weighted Manifolds
Weighted manifolds satisfy a Riemannian Penrose inequality whose equality holds precisely for unique weighted static metrics with weighted minimal boundaries, via conformal equivalence to standard static metrics.