An elliptic proof of the splitting theorems from Lorentzian geometry
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917805045055488 |
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| author | Braun, Mathias Gigli, Nicola McCann, Robert J. Ohanyan, Argam Sämann, Clemens |
| author_facet | Braun, Mathias Gigli, Nicola McCann, Robert J. Ohanyan, Argam Sämann, Clemens |
| contents | We provide a new proof of the splitting theorems from Lorentzian geometry, in which simplicity is gained by sacrificing linearity of the d'Alembertian to recover ellipticity. We exploit a negative homogeneity (non-uniformly) elliptic $p$-d'Alembert operator for this purpose. This allows us to bring the Eschenburg, Galloway, and Newman Lorentzian splitting theorems into a framework closer to the Cheeger-Gromoll splitting theorem from Riemannian geometry. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_12632 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An elliptic proof of the splitting theorems from Lorentzian geometry Braun, Mathias Gigli, Nicola McCann, Robert J. Ohanyan, Argam Sämann, Clemens Differential Geometry Mathematical Physics Analysis of PDEs Metric Geometry 83C75, 35J92 35Q75, 49Q22, 51K10, 53C21 53C50 58J05 We provide a new proof of the splitting theorems from Lorentzian geometry, in which simplicity is gained by sacrificing linearity of the d'Alembertian to recover ellipticity. We exploit a negative homogeneity (non-uniformly) elliptic $p$-d'Alembert operator for this purpose. This allows us to bring the Eschenburg, Galloway, and Newman Lorentzian splitting theorems into a framework closer to the Cheeger-Gromoll splitting theorem from Riemannian geometry. |
| title | An elliptic proof of the splitting theorems from Lorentzian geometry |
| topic | Differential Geometry Mathematical Physics Analysis of PDEs Metric Geometry 83C75, 35J92 35Q75, 49Q22, 51K10, 53C21 53C50 58J05 |
| url | https://arxiv.org/abs/2410.12632 |