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The Penrose Inequality for Metrics with Singular Sets.

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Τίτλος: The Penrose Inequality for Metrics with Singular Sets.
Συγγραφείς: Zhang, Huaiyu1 (AUTHOR) zhymath@outlook.com
Πηγή: Acta Mathematica Sinica. Sep2026, Vol. 42 Issue 9, p2394-2412. 19p.
Θεματικοί όροι: *Mathematical singularities, *Curvature, *Lipschitz continuity, *Uniqueness (Mathematics), *Hypersurfaces, *Metric spaces
Περίληψη: We study the Penrose inequality and its rigidity for metrics with singular sets. It is known that if the singular set is a hypersurface satisfying some additional conditions on its mean curvature, the metric is smooth away from the hypersurface and it is Lipschitz across the singular set, then the Penrose inequality still holds. And there are counter-examples which show that the additional conditions on the mean curvature are indispensable. As a complement, this paper studies the case of singular set of lower dimensions. We prove that the Penrose inequality still holds if the singular set is of dimensions not greater than n − 2, without any additional conditions. [ABSTRACT FROM AUTHOR]
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  – Url: https://dx.doi.org/doi:10.1007/s10114-026-4671-2
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  Data: The Penrose Inequality for Metrics with Singular Sets.
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  Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Huaiyu%22">Zhang, Huaiyu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zhymath@outlook.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Acta+Mathematica+Sinica%22">Acta Mathematica Sinica</searchLink>. Sep2026, Vol. 42 Issue 9, p2394-2412. 19p.
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  Data: *<searchLink fieldCode="DE" term="%22Mathematical+singularities%22">Mathematical singularities</searchLink><br />*<searchLink fieldCode="DE" term="%22Curvature%22">Curvature</searchLink><br />*<searchLink fieldCode="DE" term="%22Lipschitz+continuity%22">Lipschitz continuity</searchLink><br />*<searchLink fieldCode="DE" term="%22Uniqueness+%28Mathematics%29%22">Uniqueness (Mathematics)</searchLink><br />*<searchLink fieldCode="DE" term="%22Hypersurfaces%22">Hypersurfaces</searchLink><br />*<searchLink fieldCode="DE" term="%22Metric+spaces%22">Metric spaces</searchLink>
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  Data: We study the Penrose inequality and its rigidity for metrics with singular sets. It is known that if the singular set is a hypersurface satisfying some additional conditions on its mean curvature, the metric is smooth away from the hypersurface and it is Lipschitz across the singular set, then the Penrose inequality still holds. And there are counter-examples which show that the additional conditions on the mean curvature are indispensable. As a complement, this paper studies the case of singular set of lower dimensions. We prove that the Penrose inequality still holds if the singular set is of dimensions not greater than n − 2, without any additional conditions. [ABSTRACT FROM AUTHOR]
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        Value: 10.1007/s10114-026-4671-2
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      – Code: eng
        Text: English
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        PageCount: 19
        StartPage: 2394
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      – SubjectFull: Mathematical singularities
        Type: general
      – SubjectFull: Curvature
        Type: general
      – SubjectFull: Lipschitz continuity
        Type: general
      – SubjectFull: Uniqueness (Mathematics)
        Type: general
      – SubjectFull: Hypersurfaces
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      – SubjectFull: Metric spaces
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      – TitleFull: The Penrose Inequality for Metrics with Singular Sets.
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              M: 09
              Text: Sep2026
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              Y: 2026
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