4 papers · 1 filter
Intrinsic Timed Hausdorff Convergence and Its Implications
Raquel Perales
Sakovich--Sormani introduced several notions of distance between certain classes of Lorentzian manifolds. These distances use the Hausdorff and Gromov-Hausdorff distances and there…
Gromov-Hausdorff and intrinsic flat convergence of RCD(K,N) and Kato spaces
Andrea Mondino, Raquel Perales
We consider metric measure spaces satisfying the properties (ETR), (LBD), and with an almost everywhere connected regular set. In particular, these a…
Volume entropy and rigidity for RCD-spaces
Chris Connell, Xianzhe Dai, Jesús Núñez-Zimbrón +3
We develop the barycenter technique of Besson--Courtois--Gallot so that it can be applied on RCD metric measure spaces. Given a continuous map from a non-collapsed RCD$(-(N-1),…
Gromov-Hausdorff stability of tori under Ricci and integral scalar curvature bounds
Shouhei Honda, Christian Ketterer, Ilaria Mondello +2
We establish a nonlinear analogue of a splitting map into a Euclidean space, as a harmonic map into a flat torus. We prove that the existence of such a map implies Gromov-Hausdorff…