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 < 𝑝 ≤ 2, interpolate between Jauregui's mass 𝑝 = 2 and Huisken's isoperime...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2023 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
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| Онлайн доступ: | 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 |
| Цитувати: | 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 |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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 < 𝑝 ≤ 2, interpolate between Jauregui's mass 𝑝 = 2 and Huisken's isoperimetric mass, as 𝑝 → 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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| ISSN: | 1815-0659 |