8 papers
The Hawking Singularity Theorem for Hölder Continuous Metrics with -Bounded Curvature
Michael Kunzinger, Moritz Reintjes, Roland Steinbauer +1
We prove a low-regularity version of Hawking's singularity theorem for Lorentzian metrics in with Riemann curvature in , where and the dimension of spacet…
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…
On the completeness of the space
Michael Kunzinger, Norbert Ortner
We give a new proof of the completeness of the space by applying a criterion of compact regularity for the isomorphic sequence space $\lim_{k\rightarrow} (s\hat \ot…