An elliptic proof of the splitting theorems from Lorentzian geometry

Mathias Braun; Nicola Gigli; Robert J. McCann; Argam Ohanyan; Clemens Sämann

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arXiv · 2410.12632

An elliptic proof of the splitting theorems from Lorentzian geometry

Mathias Braun·Nicola Gigli·Robert J. McCann·Argam Ohanyan·Clemens Sämann

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Abstract

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.

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Mathias Braun, Nicola Gigli, Robert J. McCann, Argam Ohanyan, Clemens Sämann. 2024-10-16. An elliptic proof of the splitting theorems from Lorentzian geometry. https://arxiv.org/abs/2410.12632

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