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arXiv · 2606.03873

Positive resolution of Bartnik's cosmological splitting conjecture

Robert J. McCann·Argam Ohanyan
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Abstract

We give a proof of the cosmological splitting conjecture of Robert Bartnik from 1988, which expresses the rigidity of the cosmological Hawking--Penrose singularity theorem. It states that a timelike geodesically complete, globally hyperbolic spacetime which has compact Cauchy surfaces and satisfies the strong energy condition must split isometrically as a Lorentzian product. Our methods combine the construction of global viscosity solutions to the Lorentzian eikonal equation by Zhu--Wu--Cui with our recently developed elliptic approach to the proof of Lorentzian splitting theorems in joint work with Braun, Gigli and S\"amann, where we make use of the $p$-d'Alembertian operator for $p < 1$.

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Robert J. McCann, Argam Ohanyan. 2026-06-02. Positive resolution of Bartnik's cosmological splitting conjecture. https://arxiv.org/abs/2606.03873

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