Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature
We deal with suitable nonlinear versions of Jauregui's isocapacitary mass in 3-manifolds with nonnegative scalar curvature and compact outermost minimal boundary. These masses, which depend on a parameter 1 < ≤ 2, interpolate between Jauregui's mass = 2 and Huisken's isoperi...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212040 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature. Luca Benatti, Mattia Fogagnolo and Lorenzo Mazzieri. SIGMA 19 (2023), 091, 29 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862552358213386240 |
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| author | Benatti, Luca Fogagnolo, Mattia Mazzieri, Lorenzo |
| author_facet | Benatti, Luca Fogagnolo, Mattia Mazzieri, Lorenzo |
| citation_txt | Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature. Luca Benatti, Mattia Fogagnolo and Lorenzo Mazzieri. SIGMA 19 (2023), 091, 29 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We deal with suitable nonlinear versions of Jauregui's isocapacitary mass in 3-manifolds with nonnegative scalar curvature and compact outermost minimal boundary. These masses, which depend on a parameter 1 < ≤ 2, interpolate between Jauregui's mass = 2 and Huisken's isoperimetric mass, as → 1⁺. We derive positive mass theorems for these masses under mild conditions at infinity, and we show that these masses do coincide with the ADM mass when the latter is defined. We finally work out a nonlinear potential theoretic proof of the Penrose inequality in the optimal asymptotic regime.
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| first_indexed | 2026-03-13T05:04:08Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212040 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T05:04:08Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Benatti, Luca Fogagnolo, Mattia Mazzieri, Lorenzo 2026-01-23T10:10:45Z 2023 Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature. Luca Benatti, Mattia Fogagnolo and Lorenzo Mazzieri. SIGMA 19 (2023), 091, 29 pages 1815-0659 2020 Mathematics Subject Classification: 83C99; 35B40; 35A16; 31C15; 53C21 arXiv:2305.01453 https://nasplib.isofts.kiev.ua/handle/123456789/212040 https://doi.org/10.3842/SIGMA.2023.091 We deal with suitable nonlinear versions of Jauregui's isocapacitary mass in 3-manifolds with nonnegative scalar curvature and compact outermost minimal boundary. These masses, which depend on a parameter 1 < ≤ 2, interpolate between Jauregui's mass = 2 and Huisken's isoperimetric mass, as → 1⁺. We derive positive mass theorems for these masses under mild conditions at infinity, and we show that these masses do coincide with the ADM mass when the latter is defined. We finally work out a nonlinear potential theoretic proof of the Penrose inequality in the optimal asymptotic regime. Part of this work has been carried out during the authors’ attendance at the Thematic Program on Nonsmooth Riemannian and Lorentzian Geometry that took place at the Fields Institutein Toronto. The authors warmly thank the staff, the organizers, and the colleagues for the wonderful atmosphere and the excellent working conditions setupthere. L.B. is supported by the European Research Council’s (ERC) Project n.853404 ERC VaReg–Variational approach to the regularity of the free boundaries, financed by the program Horizon 2020, by PRA_2022_11 and by PRA_2022_14. M.F. has been supported by the European Union – Next Generation EU and by the University of Padova under the 2021 STARS Grants@Unipd programme “QuASAR”. The authors are members of Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA), which is part of the Istituto Nazionale di Alta Matematica (INdAM), and are partially funded by the GNAMPA Project “Problemi al bordo e applicazioni geometriche”. The authors are grateful to S. Hirsch and F. Oronzio for their interest in the work and for pleasant and useful conversations on the subject. The authors warmly thank the anonymous referees for their thorough reading of the paper and for the valuable suggestions that allowed them to improve the quality of the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature Article published earlier |
| spellingShingle | Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature Benatti, Luca Fogagnolo, Mattia Mazzieri, Lorenzo |
| title | Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature |
| title_full | Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature |
| title_fullStr | Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature |
| title_full_unstemmed | Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature |
| title_short | Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature |
| title_sort | nonlinear isocapacitary concepts of mass in 3-manifolds with nonnegative scalar curvature |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212040 |
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