An elliptic proof of the splitting theorems from Lorentzian geometry
Year: 2026
Type: article
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.
DOI: 10.1090/cams/77
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funders: École Polytechnique Fédérale de Lausanne, Canada Research Chairs, Österreichischen Akademie der Wissenschaften, Austrian Science Fund, Ministero dell’Istruzione, dell’Università e della Ricerca, University of Toronto, Natural Sciences and Engineering Research Council of Canada, Division of Mathematical Sciences
OpenAlex ID: W4403578418