169 citations · 512 across the 25 of their papers we have counts for
25 papers
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…
Nonlinear generalised functions on manifolds
Eduard A. Nigsch, James A. Vickers
This paper lays the foundations for a nonlinear theory of differential geometry that is developed in a subsequent paper which is based on Colombeau algebras of tensor distributions…
Green operators for low regularity spacetimes
Yafet Sanchez Sanchez, James Vickers
In this paper we define and construct advanced and retarded Green operators for the wave operator on spacetimes with low regularity. In order to do so we require that the spacetime…
Generalised hyperbolicity in spacetimes with string-like singularities
Yafet Sanchez Sanchez, James A. Vickers
In this paper we present well-posedness results of the wave equation in for spacetimes that contain string-like singularities. These results extend a framework able to char…
Generalised hyperbolicity in spacetimes with Lipschitz regularity
Yafet Sanchez Sanchez, James A. Vickers
In this paper, we obtain general conditions under which the wave equation is well-posed in spacetimes with metrics of Lipschitz regularity. In particular, the results can be applie…
The Penrose singularity theorem in regularity
Michael Kunzinger, Roland Steinbauer, James A. Vickers
We extend the validity of the Penrose singularity theorem to spacetime metrics of regularity . The proof is based on regularisation techniques, combined with recent result…