Andrea Mondino

A splitting theorem for manifolds with a convex boundary component and applications

We prove a warped product splitting theorem for manifolds with Ricci curvature bounded below, in the spirit of Croke–Kleiner [Duke Math. J. 67 (1992)]. Instead of assuming that one boundary component is compact and mean-convex, we require it to be parabolic and convex. We then de...

Lorentzian Gromov–Hausdorff convergence and pre-compactness

Abstract The goal of this paper is to introduce a notion of convergence à la Gromov–Hausdorff for Lorentzian spaces, based on 𝜀-nets formed by causal diamonds and depending solely on the time-separation function. This provides a geometric framework for convergence that applies bo...