7 papers
Maximality and Cauchy developments of Lorentzian length spaces
Olaf Müller
This article suggests the definition of "Lorentzian space" weakening the notion of Lorentzian length spaces just as much that it allows for a functor from the category of strongly…
Cheeger-Gromov compactness for manifolds with boundary
Olaf Müller
We prove Cheeger-Gromov convergence for a subsequence of a given sequence of manifolds-with-boundary of bounded geometry. The method of the proof is to reduce, via height functions…
On the Hauptvermutung of Causal Set Theory
Olaf Müller, Olaf Müller
We formulate the Hauptvermutung of Causal Set Theory in two mathematically well-defined but different ways one of which turns out to be wrong and the other one turns out to be true…
Connected holonomy is lower semicontinuous
Olaf Müller
In this article, we examine continuity properties of the maps and $\Hol^0$ assigning, on a fixed manifold , to a metric on its holonomy class resp. restricted holonom…
Orders on sets of conformal classes applied to Bartnik's conjecture
Olaf Müller
In the first part, after showing that the most natural approach to define an order on sets of conformal classes fails, we define a nontrivial order on the set of conformal…
Gromov-Hausdorff metrics and dimensions of Lorentzian length spaces
Olaf Müller
We construct analoga of Gromov-Hausdorff space for Lorentzian distances and show a Gromov precompactness result for one of them. After calculating the Dushnik-Miller dimension of M…