We prove that the Riemannian Penrose inequality holds for asymptotically flat 3-manifolds with nonnegative scalar curvature and connected horizon boundary, provided the optimal decay assumptions are met, which result in the (Formula presented.) mass being a well-defined geometric invariant. Our proof builds on a novel interplay between the Hawking mass and a potential-theoretic version of it, recently introduced by Agostiniani, Oronzio, and the third named author. As a consequence, we establish the equality between (Formula presented.) mass and Huisken's isoperimetric mass under the above sharp assumptions. Moreover, we establish a Riemannian Penrose inequality in terms of the isoperimetric mass on any 3-manifold with nonnegative scalar curvature, connected horizon boundary, and which supports a well-posed notion of weak inverse mean curvature flow (IMCF). In particular, such isoperimetric Riemannian Penrose inequality does not require the asymptotic flatness of the manifold. The argument is based on a new asymptotic comparison result involving Huisken's isoperimetric mass and the Hawking mass.

On the isoperimetric Riemannian Penrose inequality / Benatti, Luca; Fogagnolo, Mattia; Mazzieri, Lorenzo. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 2024:(2024). [10.1002/cpa.22239]

On the isoperimetric Riemannian Penrose inequality

Benatti, Luca;Fogagnolo, Mattia;Mazzieri, Lorenzo
2024-01-01

Abstract

We prove that the Riemannian Penrose inequality holds for asymptotically flat 3-manifolds with nonnegative scalar curvature and connected horizon boundary, provided the optimal decay assumptions are met, which result in the (Formula presented.) mass being a well-defined geometric invariant. Our proof builds on a novel interplay between the Hawking mass and a potential-theoretic version of it, recently introduced by Agostiniani, Oronzio, and the third named author. As a consequence, we establish the equality between (Formula presented.) mass and Huisken's isoperimetric mass under the above sharp assumptions. Moreover, we establish a Riemannian Penrose inequality in terms of the isoperimetric mass on any 3-manifold with nonnegative scalar curvature, connected horizon boundary, and which supports a well-posed notion of weak inverse mean curvature flow (IMCF). In particular, such isoperimetric Riemannian Penrose inequality does not require the asymptotic flatness of the manifold. The argument is based on a new asymptotic comparison result involving Huisken's isoperimetric mass and the Hawking mass.
2024
Benatti, Luca; Fogagnolo, Mattia; Mazzieri, Lorenzo
On the isoperimetric Riemannian Penrose inequality / Benatti, Luca; Fogagnolo, Mattia; Mazzieri, Lorenzo. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 2024:(2024). [10.1002/cpa.22239]
File in questo prodotto:
File Dimensione Formato  
Comm Pure Appl Math - 2024 - Benatti - On the isoperimetric Riemannian Penrose inequality.pdf

accesso aperto

Descrizione: online first
Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Creative commons
Dimensione 426.33 kB
Formato Adobe PDF
426.33 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/440414
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
  • OpenAlex ND
social impact