27 citations · 135 across the 15 of their papers we have counts for
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A conformal Hopf-Rinow theorem for semi-Riemannian spacetimes
Annegret Burtscher
The famous Hopf-Rinow Theorem states, amongst others, that a Riemannian manifold is metrically complete if and only if it is geodesically complete. The Clifton-Pohl torus fails to…
Global Hyperbolicity through the Eyes of the Null Distance
Annegret Burtscher, Leonardo García-Heveling
No Hopf-Rinow Theorem is possible in Lorentzian Geometry. Nonetheless, we prove that a spacetime is globally hyperbolic if and only if it is metrically complete with respect to the…
Variations of Weyl's tube formula
Annegret Burtscher, Gert Heckman
In 1939 Weyl showed that the volume of spherical tubes around compact submanifolds M of Euclidean space depends solely on the induced Riemannian metric on M. Can this intrinsic nat…
Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary
Annegret Burtscher, Christian Ketterer, Robert J. McCann +1
Consider an essentially nonbranching metric measure space with the measure contraction property of Ohta and Sturm, or with a Ricci curvature lower bound in the sense of Lott, Sturm…
Properties of the Null Distance and Spacetime Convergence
Brian Allen, Annegret Burtscher
The null distance for Lorentzian manifolds was recently introduced by Sormani and Vega. Under mild assumptions on the time function of the spacetime, the null distance gives rise t…
Length structures on manifolds with continuous Riemannian metrics
Annegret Y. Burtscher
It is well-known that the class of piecewise smooth curves together with a smooth Riemannian metric induces a metric space structure on a manifold. However, little is known about t…