21 citations · 44 across the 6 of their papers we have counts for
8 papers
Generalized cones as Lorentzian length spaces: Causality, curvature, and singularity theorems
Stephanie B. Alexander, Melanie Graf, Michael Kunzinger +1
We study generalizations of Lorentzian warped products with one-dimensional base of the form , where is an interval, is a length space and is a positive co…
Space-time convex functions and sectional curvature
Stephanie B. Alexander, William A. Karr
We show that in Lorentzian manifolds, sectional curvature bounds of the form , as defined by Andersson and Howard, are closely tied to space-time convex and …
Convex Functions and Geodesic Connectedness of Space-times
Stephanie B. Alexander, William A. Karr
This paper explores the relation between convex functions and the geometry of space-times and semi-Riemannian manifolds (an investigation initiated by Gibbons-Ishibashi). Specifica…
Warped products admitting a curvature bound
Stephanie B. Alexander, Richard L. Bishop
This paper completes a fundamental construction in Alexandrov geometry. Previously we gave a new construction of metric spaces with curvature bounds either above or below, namely w…
An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds
Stephanie Alexander, Vitali Kapovitch, Anton Petrunin
It is proved that a convex hypersurface in a Riemannian manifold of sectional curvature at least k is an Alexandrov's space of curvature at least k. This theorem provides an optima…
Alexandrov meets Kirszbraun
Stephanie Alexander, Vitali Kapovitch, Anton Petrunin
We give a simplified proof of the generalized Kirszbraun theorem for Alexandrov spaces, which is due to Lang and Schroeder. We also discuss related questions, both solved and open.