91 citations · 439 across the 28 of their papers we have counts for
29 papers
Identifiability of Polynomial Models from First Principles and via a Gröbner Basis Approach
Janet D. Godolphin, James D. E. Grant
The relationship between a set of design points and the class of hierarchical polynomial models identifiable from the design is investigated. Saturated models are of particular int…
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…
The Hawking-Penrose singularity theorem for -Lorentzian metrics
Melanie Graf, James D. E. Grant, Michael Kunzinger +1
We show that the Hawking--Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of $C^…
A positive mass theorem for low-regularity Riemannian metrics
James D. E. Grant, Nathalie Tassotti
We show that the positive mass theorem holds for continuous Riemannian metrics that lie in the Sobolev space for manifolds of dimension less than or equal to …
On differentiability of volume time functions
Piotr T. Chruściel, James D. E. Grant, Ettore Minguzzi
We show differentiability of a class of Geroch's volume functions on globally hyperbolic manifolds. Furthermore, we prove that every volume function satisfies a local anti-Lipschit…