117 citations · 882 across the 65 of their papers we have counts for
16 papers · 1 filter
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…
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…
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…
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…
On curvature bounds in Lorentzian length spaces
Tobias Beran, Michael Kunzinger, Felix Rott
We introduce several new notions of (sectional) curvature bounds for Lorentzian pre-length spaces: On the one hand, we provide convexity/concavity conditions for the (modified) tim…
Synthetic versus distributional lower Ricci curvature bounds
Michael Kunzinger, Michael Oberguggenberger, James A. Vickers
We compare two standard approaches to defining lower Ricci curvature bounds for Riemannian metrics of regularity below . These are, on the one hand, the synthetic definition v…
Null distance and convergence of Lorentzian length spaces
Michael Kunzinger, Roland Steinbauer
The null distance of Sormani and Vega encodes the manifold topology as well as the causality structure of a (smooth) spacetime. We extend this concept to Lorentzian length spaces,…
The future is not always open
James D. E. Grant, Michael Kunzinger, Clemens Sämann +1
We demonstrate the breakdown of several fundamentals of Lorentzian causality theory in low regularity. Most notably, chronological futures (defined naturally using locally Lipschit…
Inextendibility of spacetimes and Lorentzian length spaces
James D. E. Grant, Michael Kunzinger, Clemens Sämann
We study the low-regularity (in-)extendibility of spacetimes within the synthetic-geometric framework of Lorentzian length spaces developed in [KS:17]. To this end, we introduce ap…
Lorentzian length spaces
Michael Kunzinger, Clemens Sämann
We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The rôle of the metric is taken over by the time separation fu…
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'.…
A regularization approach to non-smooth symplectic geometry
Guenther Hoermann, Sanja Konjik, Michael Kunzinger
We introduce non-smooth symplectic forms on manifolds and describe corresponding Poisson structures on the algebra of Colombeau generalized functions. This is achieved by establish…
A regularisation approach to causality theory for -Lorentzian metrics
Michael Kunzinger, Roland Steinbauer, James A. Vickers +1
We show that many standard results of Lorentzian causality theory remain valid if the regularity of the metric is reduced to . Our approach is based on regularisations of…
The exponential map of a -metric
Michael Kunzinger, Roland Steinbauer, Milena Stojkovic
Given a pseudo-Riemannian metric of regularity on a smooth manifold, we prove that the corresponding exponential map is a bi-Lipschitz homeomorphism locally around any po…
Global Gronwall Estimates for Integral Curves on Riemannian Manifolds
Michael Kunzinger, Hermann Schichl, Roland Steinbauer +1
We prove Gronwall-type estimates for the distance of integral curves of smooth vector fields on a Riemannian manifold. Such estimates are of central importance for all methods of s…