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An elliptic proof of the splitting theorems from Lorentzian geometry
[Submitted on 16 Oct 2024 (v1), last revised 11 Jun 2026 (this v · 2026-06-15 · via math updates on arXiv.org

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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.

Submission history

From: Argam Ohanyan [view email]
[v1] Wed, 16 Oct 2024 14:53:13 UTC (35 KB)
[v2] Thu, 11 Jun 2026 20:29:41 UTC (139 KB)