Mass-type invariants in the presence of a cosmological constant
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911624797880320 |
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| author | Agostiniani, Virginia Borghini, Stefano Mazzieri, Lorenzo |
| author_facet | Agostiniani, Virginia Borghini, Stefano Mazzieri, Lorenzo |
| contents | In this paper, we introduce a new family of mass-type invariants for time-symmetric initial data in space-times satisfying the Dominant Energy Condition. For positive cosmological constant, these invariants, unlike the total Hawking mass, turn out to be genuinely effective in providing new characterizations of the de Sitter solution. From a theoretical standpoint, this opens a new perspective on how one might refine the rigidity statement originally proposed by Min-Oo in his well known conjecture, later refuted by the counterexamples of Brendle, Marques, and Neves. Via a formal limiting procedure, we also define another invariant, the 1-harmonic Mass, for which we independently prove a positive mass theorem and a Penrose-type inequality, thereby extending tools for probing space-time geometries in the presence of a positive cosmological constant. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_01543 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mass-type invariants in the presence of a cosmological constant Agostiniani, Virginia Borghini, Stefano Mazzieri, Lorenzo Differential Geometry General Relativity and Quantum Cosmology Analysis of PDEs 53C21, 31C12, 53C24, 53Z05 In this paper, we introduce a new family of mass-type invariants for time-symmetric initial data in space-times satisfying the Dominant Energy Condition. For positive cosmological constant, these invariants, unlike the total Hawking mass, turn out to be genuinely effective in providing new characterizations of the de Sitter solution. From a theoretical standpoint, this opens a new perspective on how one might refine the rigidity statement originally proposed by Min-Oo in his well known conjecture, later refuted by the counterexamples of Brendle, Marques, and Neves. Via a formal limiting procedure, we also define another invariant, the 1-harmonic Mass, for which we independently prove a positive mass theorem and a Penrose-type inequality, thereby extending tools for probing space-time geometries in the presence of a positive cosmological constant. |
| title | Mass-type invariants in the presence of a cosmological constant |
| topic | Differential Geometry General Relativity and Quantum Cosmology Analysis of PDEs 53C21, 31C12, 53C24, 53Z05 |
| url | https://arxiv.org/abs/2603.01543 |