The total geodesic curvature and the $(2+1)$-dimensional hyperbolic mass
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914325623472128 |
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| author | He, Xiaokai Wu, Xiaoning Xie, Naqing |
| author_facet | He, Xiaokai Wu, Xiaoning Xie, Naqing |
| contents | We consider a Jordan domain diffeomorphic to a closed two-dimensional disk with a smooth boundary. Assuming the Gauss curvature of the domain has a negative lower bound, the Gauss-Bonnet formula provides an upper bound for the total geodesic curvature of the boundary curve. This bound, however, inherently depends on the interior geometry of the region. In this paper, we derive an upper bound for the total geodesic curvature expressed solely in terms of the boundary data. Notably, the proof is connected to the positivity of the hyperbolic Hamiltonian mass in the (2+1)-dimensional gravity theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11900 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The total geodesic curvature and the $(2+1)$-dimensional hyperbolic mass He, Xiaokai Wu, Xiaoning Xie, Naqing Differential Geometry General Relativity and Quantum Cosmology 53C21 We consider a Jordan domain diffeomorphic to a closed two-dimensional disk with a smooth boundary. Assuming the Gauss curvature of the domain has a negative lower bound, the Gauss-Bonnet formula provides an upper bound for the total geodesic curvature of the boundary curve. This bound, however, inherently depends on the interior geometry of the region. In this paper, we derive an upper bound for the total geodesic curvature expressed solely in terms of the boundary data. Notably, the proof is connected to the positivity of the hyperbolic Hamiltonian mass in the (2+1)-dimensional gravity theory. |
| title | The total geodesic curvature and the $(2+1)$-dimensional hyperbolic mass |
| topic | Differential Geometry General Relativity and Quantum Cosmology 53C21 |
| url | https://arxiv.org/abs/2602.11900 |