Peer-reviewedCC BY-NC-NDCommunications of the American Mathematical Society
An elliptic proof of the splitting theorems from Lorentzian geometry
Abstract
We initiate the development of a theory of the negative homogeneity p p -d’Alembert operator in the smooth setting. We relate it to a Bochner-Ohta identity of homogeneity 2 p − 2 > 0 2p-2>0 . We identify conditions under which the unexpected ellipticity of this operator turns out to be uniform. We exploit this to give a new proof of the Eschenburg, Galloway and Newman splitting theorems from Lorentzian geometry, which allows us bring them into a framework closer to the Cheeger-Gromoll splitting theorem from Riemannian geometry.
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BibTeX
@article{braun2026elliptic,
title = {{An elliptic proof of the splitting theorems from Lorentzian geometry}},
author = {Mathias Braun and Nicola Gigli and Robert J. McCann and Argam Ohanyan and Clemens Sämann},
journal = {Communications of the American Mathematical Society},
year = {2026},
month = aug,
doi = {10.1090/cams/77},
url = {https://doi.org/10.1090/cams/77},
note = {CC BY-NC-ND},
}
RIS
TY - JOUR
TI - An elliptic proof of the splitting theorems from Lorentzian geometry
AU - Mathias Braun
AU - Nicola Gigli
AU - Robert J. McCann
AU - Argam Ohanyan
AU - Clemens Sämann
PY - 2026
DA - 2026/08/10
JO - Communications of the American Mathematical Society
DO - 10.1090/cams/77
UR - https://doi.org/10.1090/cams/77
AB - We initiate the development of a theory of the negative homogeneity p p -d’Alembert operator in the smooth setting. We relate it to a Bochner-Ohta identity of homogeneity 2 p − 2 > 0 2p-2>0 . We identify conditions under which the unexpected ellipticity of this operator turns out to be uniform. We exploit this to give a new proof of the Eschenburg, Galloway and Newman splitting theorems from Lorentzian geometry, which allows us bring them into a framework closer to the Cheeger-Gromoll splitting theorem from Riemannian geometry.
SN - 2692-3688
ER -