8 papers · 1 filter
Distributional sectional curvature bounds for Riemannian metrics of low regularity
Darius Erös, Michael Kunzinger, Argam Ohanyan +1
Sectional curvature bounds are of central importance in the study of Riemannian manifolds, both in smooth differential geometry and in the generalized synthetic setting of Alexandr…
Timelike conjugate points in Lorentzian length spaces
James D. E. Grant, Michael Kunzinger, Argam Ohanyan +2
We study notions of conjugate points along timelike geodesics in the synthetic setting of Lorentzian (pre-)length spaces, inspired by earlier work for metric spaces by Shankar--Sor…
Hawking's singularity theorem for Lipschitz Lorentzian metrics
Matteo Calisti, Melanie Graf, Eduardo Hafemann +2
We prove Hawking's singularity theorem for spacetime metrics of local Lipschitz regularity. The proof rests on (1) new estimates for the Ricci curvature of regularising smooth metr…
Ricci curvature bounds and rigidity for non-smooth Riemannian and semi-Riemannian metrics
Michael Kunzinger, Argam Ohanyan, Alessio Vardabasso
We study rigidity problems for Riemannian and semi-Riemannian manifolds with metrics of low regularity. Specifically, we prove a version of the Cheeger-Gromoll splitting theorem \c…
Lie Transformation Groups -- An Introduction to Symmetry Group Analysis of Differential Equations
Michael Kunzinger
These are lecture notes of a course on symmetry group analysis of differential equations, based mainly on P. J. Olver's book 'Applications of Lie Groups to Differential Equations'.…
The equivalence of smooth and synthetic notions of timelike sectional curvature bounds
Tobias Beran, Michael Kunzinger, Argam Ohanyan +1
Timelike sectional curvature bounds play an important role in spacetime geometry, both for the understanding of classical smooth spacetimes and for the study of Lorentzian (pre-)le…