Abstract
AbstractWe establish a new uniqueness theorem for the three dimensional Schwarzschild–de Sitter metrics. For this, some new or improved tools are developed. These include a reverse Łojasiewicz inequality, which holds in a neighborhood of the extremal points of any smooth function. We further prove the smoothness of the set of maxima of the lapse, whenever this set contains a topological hypersurface. This leads to a new strategy for the classification of well behaved static solutions of vacuum Einstein equations with a positive cosmological constant, based on the geometry of the maximum-set of the lapse.
Funder
Austrian Science Fund
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Polish National Center of Science
Publisher
Springer Science and Business Media LLC
Subject
Mechanical Engineering,Mathematics (miscellaneous),Analysis
Reference52 articles.
1. Abate, M., Tovena, F.: Geometria differenziale, volume 54 of Unitext. Springer, Milan, (2011). La Matematica per il 3+2.
2. Agostiniani, V., Borghini, S., Mazzieri, L.: On the Serrin problem for ring-shaped domains. (2021). ArXiv Preprint Server arXiv:2109.11255
3. Agostiniani, V., Mazzieri, L.: On the Geometry of the Level Sets of Bounded Static Potentials. Comm. Math. Phys. 355(1), 261–301, 2017
4. Ambrozio, L.: On static three-manifolds with positive scalar curvature. Journal of Differential Geometry 107(1), 1–45, 2017
5. Baltazar, H., Batista, R., Ribeiro Jr, E.: Geometric inequalities for critical metrics of the volume functional. (2018). ArXiv Preprint Server arXiv:1810.09313
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