27 citations · 135 across the 15 of their papers we have counts for
15 papers
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…
Time functions on Lorentzian length spaces
Annegret Burtscher, Leonardo García-Heveling
In general relativity, time functions are crucial objects whose existence and properties are intimately tied to the causal structure of a spacetime and also to the initial value fo…
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…
Initial data and black holes for matter models
Annegret Y. Burtscher
To observe the dynamic formation of black holes in general relativity, one essentially needs to prove that closed trapped surfaces form during evolution from initial data that do n…
Weak second Bianchi identity for static, spherically symmetric spacetimes with timelike singularities
Annegret Burtscher, Michael K. -H. Kiessling, A. Shadi Tahvildar-Zadeh
The (twice-contracted) second Bianchi identity is a differential curvature identity that holds on any smooth manifold with a metric. In the case when such a metric is Lorentzian an…
On the asymptotic behavior of static perfect fluids
Lars Andersson, Annegret Y. Burtscher
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state.…
Hyperboloidal evolution and global dynamics for the focusing cubic wave equation
Annegret Y. Burtscher, Roland Donninger
The focusing cubic wave equation in three spatial dimensions has the explicit solution . We study the stability of the blowup described by this solution as wi…
The formation of trapped surfaces in spherically-symmetric Einstein-Euler spacetimes with bounded variation
Annegret Y. Burtscher, Philippe G. LeFloch
We study the evolution of a self-gravitating compressible fluid in spherical symmetry and we prove the existence of weak solutions with bounded variation for the Einstein-Euler equ…
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…
New energy inequalities for tensorial wave equations on spacetimes that satisfy a one-sided bound
Annegret Y. Burtscher, James D. E. Grant, Philippe G. LeFloch
We consider several tensorial wave equations, specifically the equations of Maxwell, Yang-Mills, and Weyl fields, posed on a curved spacetime, and we establish new energy inequalit…
Algebras of generalized functions with smooth parameter dependence
Annegret Burtscher, Michael Kunzinger
We show that spaces of Colombeau generalized functions with smooth parameter dependence are isomorphic to those with continuous parametrization. Based on this result we initiate a…
An algebraic approach to manifold-valued generalized functions
Annegret Burtscher
We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with inverti…