Fetching the paper…
Reading the bibliography…
We give a simplified approach to Kunzinger & Saemann's theory of Lorentzian length spaces in the globally hyperbolic case; these provide a nonsmooth framework for general relativity.
The existence of complete Riemannian metrics
Katsumi Nomizu and Hideki Ozeki · 1961
Earlier work this paper cites.
Gravitational collapse and space-time singularities
Roger Penrose · 1965
Earlier work this paper cites.
On the structure of causal spaces
E. H. Kronheimer and R. Penrose · 1967
Earlier work this paper cites.
Spinor structure of space-times in general relativity. I
Robert Geroch · 1968
Earlier work this paper cites.
Black holes in general relativity
S. W. Hawking · 1972
Earlier work this paper cites.
The large scale structure of space-time
S. W. Hawking and G. F. R. Ellis · 1973
Earlier work this paper cites.
Differential topology
Victor Guillemin and Alan Pollack · 1974
Earlier work this paper cites.
Diffusions hypercontractives
D. Bakry and Michel Émery · 1985
Earlier work this paper cites.
Global Lorentzian geometry
John K. Beem, Paul E. Ehrlich, and Kevin L. Easley · 1996
Earlier work this paper cites.
Comparison and rigidity theorems in semi-Riemannian geometry
Lars Andersson and Ralph Howard · 1998
Earlier work this paper cites.
Maximum principles for null hypersurfaces and null splitting theorems
Gregory J. Galloway · 2000
Earlier work this paper cites.
A course in metric geometry
Dmitri Burago, Yuri Burago, and Sergei Ivanov · 2001
Earlier work this paper cites.
Uniqueness and transport density in Monge’s transportation problem
M. Feldman and R.J. McCann · 2002
Earlier work this paper cites.
A new topology on the space of Lorentzian metrics on a fixed manifold
Johan Noldus · 2002
Earlier work this paper cites.
Topics in Optimal Transportation
C. Villani · 2003
Earlier work this paper cites.
The moduli space of isometry classes of globally hyperbolic spacetimes
Luca Bombelli and Johan Noldus · 2004
Earlier work this paper cites.
Spacetime and geometry
Sean Carroll · 2004
Earlier work this paper cites.
Fabio Cavalletti and Andrea Mondino · 2004
Earlier work this paper cites.
The limit space of a Cauchy sequence of globally hyperbolic spacetimes
Johan Noldus · 2004
Earlier work this paper cites.
A Lorentzian Gromov-Hausdorff notion of distance
Johan Noldus · 2004
Earlier work this paper cites.
On the geometry of metric measure spaces. I
Karl-Theodor Sturm · 2006
Earlier work this paper cites.
On the geometry of metric measure spaces. II
Karl-Theodor Sturm · 2006
Cited alongside, same era.
Lorentz and semi-Riemannian spaces with Alexandrov curvature bounds
Stephanie B. Alexander and Richard L. Bishop · 2008
Cited alongside, same era.
Ricci curvature for metric-measure spaces via optimal transport
John Lott and Cédric Villani · 2009
Cited alongside, same era.
Optimal Transport. Old and New
C. Villani · 2009
Cited alongside, same era.
Localization and tensorization properties of the curvature-dimension condition for metric measure spaces
Kathrin Bacher and Karl-Theodor Sturm · 2010
Cited alongside, same era.
Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor
Jeffrey S. Case · 2010
Cited alongside, same era.
Inscribed radius bounds for lower Ricci bounded metric measure spaces with mean convex boundary
Annegret Burtscher, Christian Ketterer, Robert J. McCann, and Eric Woolgar · 2020
Later among the works it cites.
Singularity theorems for C 1 C^{1} -Lorentzian metrics
Melanie Graf · 2020
Later among the works it cites.
Displacement convexity of Boltzmann’s entropy characterizes the strong energy condition from general relativity
Robert J. McCann · 2020
Later among the works it cites.
Distribution-valued Ricci bounds for metric measure spaces, singular time changes, and gradient estimates for Neumann heat flows
Karl-Theodor Sturm · 2020
Later among the works it cites.
Independence of synthetic curvature dimension conditions on transport distance exponent
Afiny Akdemir, Andrew Colinet, Robert McCann, Fabio Cavalletti, and Flavia Santarcangelo · 2021
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A user’s guide to optimal transport
Luigi Ambrosio and Nicola Gigli · 2013
Cited alongside, same era.
Topological censorship from the initial data point of view
Michael Eichmair, Gregory J. Galloway, and Daniel Pollack · 2013
Cited alongside, same era.
Scalar-tensor gravitation and the Bakry-Émery-Ricci tensor
Eric Woolgar · 2013
Cited alongside, same era.
Metric measure spaces with Riemannian Ricci curvature bounded from below
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2014
Cited alongside, same era.
Non-branching geodesics and optimal maps in strong C D ( K , ∞ ) CD(K,\infty) -spaces
Tapio Rajala and Karl-Theodor Sturm · 2014
Cited alongside, same era.
On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces
Matthias Erbar, Kazumasa Kuwada, and Karl-Theodor Sturm · 2015
Cited alongside, same era.
Uniqueness of curvature measures in pseudo-Riemannian geometry
Andreas Bernig, Dmitry Faifman, and Gil Solanes · 2021
Later among the works it cites.
Optimal transport, gradient estimates, and pathwise Brownian coupling on spaces with variable Ricci bounds
Mathias Braun, Karen Habermann, and Karl-Theodor Sturm · 2021
Later among the works it cites.
The globalization theorem for the curvature-dimension condition
Fabio Cavalletti and Emanuel Milman · 2021
Later among the works it cites.
Holder Continuity of Tangent Cones and Non-Branching in RCD(K,N) Spaces
Qin Deng · 2021
Later among the works it cites.
A Bakry-Émery almost splitting result with applications to the topology of black holes
Gregory J. Galloway, Marcus A. Khuri, and Eric Woolgar · 2021
Later among the works it cites.
Foundations of general relativity, from Einstein to black holes
Klaas Landsman · 2021
Later among the works it cites.
Singularities, black holes, and cosmic censorship: a tribute to Roger Penrose
Klaas Landsman · 2021
Later among the works it cites.
Properties of the null distance and spacetime convergence
Brian Allen and Annegret Burtscher · 2022
Later among the works it cites.
Curvature measures of pseudo-Riemannian manifolds
Andreas Bernig, Dmitry Faifman, and Gil Solanes · 2022
Later among the works it cites.
A review of Lorentzian synthetic theory of timelike Ricci curvature bounds
Fabio Cavalletti and Andrea Mondino · 2022
Later among the works it cites.
Null distance and convergence of Lorentzian length spaces
Michael Kunzinger and Roland Steinbauer · 2022
Later among the works it cites.
Good geodesics satisfying the timelike curvature dimension condition
Mathias Braun · 2023
Closest in time.
Rényi’s entropy on Lorentzian spaces. Timelike curvature dimension conditions
Mathias Braun · 2023
Closest in time.
Characterization of null energy via displacement convexity of entropy
Christian Ketterer · 2023
Closest in time.
An optimal transport formulation of the Einstein equations of general relativity
Andrea Mondino and Stefan Suhr · 2023
Closest in time.