Cosmological rigidity via p-harmonic temporal functions
Abstract
We prove a splitting theorem for cosmological spacetimes which admit a globally p-harmonic Cauchy temporal function for some p < 1, without making any use of timelike lines. In Bartnik's context of cosmological and timelike geodesically complete spacetimes, we establish a Liouville-type unboundedness result which shows that globally p-harmonic temporal functions, p < 1, are necessarily Cauchy temporal. Moreover, using the theory of elliptic PDEs, we show that locally Lipschitz p-harmonic temporal functions with p < 1 are in fact smooth. Altogether, our work reduces the resolution of Bartnik's cosmological splitting conjecture to the global weak solvability of the p-d'Alembert equation for some p < 1 in the class of locally Lipschitz temporal functions.
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BibTeX
@misc{ohanyan2026cosmological,
title = {{Cosmological rigidity via $p$-harmonic temporal functions}},
author = {Argam Ohanyan},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01456},
eprint = {2611.01456},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01456},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cosmological rigidity via p-harmonic temporal functions
AU - Argam Ohanyan
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01456
UR - https://arxiv.org/abs/2611.01456
AB - We prove a splitting theorem for cosmological spacetimes which admit a globally p-harmonic Cauchy temporal function for some p < 1, without making any use of timelike lines. In Bartnik's context of cosmological and timelike geodesically complete spacetimes, we establish a Liouville-type unboundedness result which shows that globally p-harmonic temporal functions, p < 1, are necessarily Cauchy temporal. Moreover, using the theory of elliptic PDEs, we show that locally Lipschitz p-harmonic temporal functions with p < 1 are in fact smooth. Altogether, our work reduces the resolution of Bartnik's cosmological splitting conjecture to the global weak solvability of the p-d'Alembert equation for some p < 1 in the class of locally Lipschitz temporal functions.
ER -