Λεπτομέρειες βιβλιογραφικής εγγραφής
| 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] |
| Βάση Δεδομένων: |
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