1 citations · 1 across the 5 of their papers we have counts for
9 papers
Causal Sobolev spaces and gradient flows
Mathias Braun, Nicola Gigli, Robert McCann +1
We develop a relaxation-based approach to Sobolev functions and Cheeger energies on metric spacetimes, in analogy with the construction used in positive signature. For an exponent…
Almost-splitting of spacetimes under timelike sectional curvature bounds
Nicola Gigli, Melanie Graf, Robert J. McCann +3
We establish an almost-splitting theorem for spacetimes under timelike sectional curvature bounds in the spirit of the celebrated Riemannian result due to Cheeger and Colding. More…
Positive resolution of Bartnik's cosmological splitting conjecture
Robert J. McCann, Argam Ohanyan
We give a proof of the cosmological splitting conjecture of Robert Bartnik from 1988, which expresses the rigidity of the cosmological Hawking--Penrose singularity theorem. It stat…
Failure of local equi-Lipschitzness for families of Lorentz distances to Cauchy surface foliations
Gregory J. Galloway, Robert J. McCann, Argam Ohanyan
The families of Lorentzian distance functions to and from points along a complete timelike line in a spacetime are known to be locally equi-Lipschitz continuous in a neighborhood o…
A Lorentzian splitting theorem for continuously differentiable metrics and weights
Mathias Braun, Nicola Gigli, Robert J. McCann +2
We prove a splitting theorem for globally hyperbolic, weighted spacetimes with metrics and weights of regularity by combining elliptic techniques for the negative homogeneity…
Trading linearity for ellipticity: a nonsmooth approach to Einstein's theory of gravity and the Lorentzian splitting theorems
Robert J. McCann
While Einstein's theory of gravity is formulated in a smooth setting, the celebrated singularity theorems of Hawking and Penrose describe many physical situations in which this smo…
An elliptic proof of the splitting theorems from Lorentzian geometry
Mathias Braun, Nicola Gigli, Robert J. McCann +2
We provide a new proof of the splitting theorems from Lorentzian geometry, in which simplicity is gained by sacrificing linearity of the d'Alembertian to recover ellipticity. We ex…
A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes
Tobias Beran, Mathias Braun, Matteo Calisti +5
We introduce a variational first-order Sobolev calculus on metric measure spacetimes. The key object is the maximal weak subslope of an arbitrary causal function, which plays the r…
Causal convergence conditions through variable timelike Ricci curvature bounds
Mathias Braun, Robert J. McCann
We describe a nonsmooth notion of globally hyperbolic, regular length metric spacetimes . It is based on ideas of Kunzinger-Sämann, but does not require Lipschitz c…