Robert McCann – University of Toronto
Wednesday, June 24, 2026
Zoom opens: 10:30AM EDT
Seminar begins: 10:45AM EDT
Trading linearity for ellipticity: a low regularity Lorentzian splitting theorem
While Einstein's theory of gravity is formulated in a smooth setting, the celebrated singularity theorems of Hawking and Penrose describe many physical situations in which this smoothness must eventually breakdown. It is thus of great interest to study the theory in low regularity settings. In the lecture, we establish a low regularity splitting theorem by sacrificing linearity of the d'Alembertian to recover ellipticity. We exploit a negative homogeneity $p$-d'Alembert operator for this purpose. The same technique yields a simplified proof of Eschenberg (1988) Galloway (1989) and Newman's (1990) confirmation of Yau's (1982) conjecture, bringing all three Lorentzian splitting results into a framework closer to the Cheeger-Gromoll splitting theorem from Riemannian geometry. Based on joint work with Mathias Braun, Nicola Gigli, Argam Ohanyan, and Clemens Saemann: 1) arXiv 2501.00702 2) arXiv 2408.15968 3) arXiv 2410.12632 4) arXiv 2507.06836