A new proof of the Riemannian Penrose inequality

Virginia Agostiniani; Carlo Mantegazza; Lorenzo Mazzieri; Francesca Oronzio

doi:10.4171/rlm/1024

JournalsrlmVol. 34, No. 3pp. 715–726

A new proof of the Riemannian Penrose inequality

Virginia Agostiniani
Università di Trento, Povo, Italy
Carlo Mantegazza
Università di Napoli Federico II, Italy
- MathSciNet
- zbMATH Open
Lorenzo Mazzieri
Università di Trento, Povolo, Italy
Francesca Oronzio
Sapienza Università di Roma, Italy
- MathSciNet
- zbMATH Open

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Abstract

We give an overview of our recent new proof of the Riemannian Penrose inequality in the case of a single black hole. The proof is based on a new monotonicity formula, holding along the level sets of the $p$ -capacitary potential of the connected boundary of an asymptotically flat $3$ -manifold, with nonnegative scalar curvature.

Cite this article

Virginia Agostiniani, Carlo Mantegazza, Lorenzo Mazzieri, Francesca Oronzio, A new proof of the Riemannian Penrose inequality. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 34 (2023), no. 3, pp. 715–726

DOI 10.4171/RLM/1024