16 citations · 70 across the 19 of their papers we have counts for
13 papers · 1 filter
Hausdorff-type metric geometry of the space of Cauchy hypersurfaces
Christian Lange, Jonas W. Peteranderl
We equip the space of Cauchy hypersurfaces in a globally hyperbolic spacetime with a natural Hausdorff-type metric. For a timelike Cauchy complete, smooth Lorentzian manifold with…
Orbifolds and manifold quotients with upper curvature bounds
Christian Lange
We characterize Riemannian orbifolds with an upper curvature bound in the Alexandrov sense as reflectofolds, i.e. Riemannian orbifolds all of whose local groups are generated by re…
On continuous billiard and quasigeodesic flows characterizing alcoves and isosceles tetrahedra
Christian Lange
We characterize fundamental domains of affine reflection groups as those polyhedral convex bodies which support a continuous billiard dynamics. We interpret this characterization i…
How highly connected can an orbifold be?
Christian Lange, Marco Radeschi
On the one hand, we provide the first examples of arbitrarily highly connected (compact) bad orbifolds. On the other hand, we show that n-connected n-orbifolds are manifolds. The l…
Sharp systolic inequalities for rotationally symmetric 2-orbifolds
Christian Lange, Tobias Soethe
We show that suitably defined systolic ratios are globally bounded from above on the space of rotationally symmetric spindle orbifolds and that the upper bound is attained precisel…
Lorentz meets Lipschitz
Christian Lange, Alexander Lytchak, Clemens Sämann
We show that maximal causal curves for a Lipschitz continuous Lorentzian metric admit a -parametrization and that they solve the geodesic equation in the sense o…
Closed geodesics on compact orbifolds and on noncompact manifolds
Christian Lange, Christoph Zwickler
We prove the existence of a nonconstant closed geodesic on every odd-dimensional compact Riemannian orbifold and on every connected, noncontractible Riemannian manifold that admits…
Deformations of the Veronese embedding and Finsler 2-spheres of constant curvature
Christian Lange, Thomas Mettler
We establish a one-to-one correspondence between Finsler structures on the -sphere with constant curvature and all geodesics closed on the one hand, and Weyl connections on…
Odd-dimensional orbifolds with all geodesics closed are covered by manifolds
Manual Amann, Christian Lange, Marco Radeschi
Manifolds all of whose geodesics are closed have been studied a lot, but there are only few examples known. The situation is different if one allows in addition for orbifold singul…
Orbifolds from a metric viewpoint
Christian Lange
We characterize Riemannian orbifolds and their coverings in terms of metric geometry. In particular, we show that the metric double of a Riemannian orbifold along the closure of it…
On the existence of closed geodesics on 2-orbifolds
Christian Lange
We show that on every compact Riemannian 2-orbifold there exist infinitely many closed geodesics of positive length.
A Hamiltonian version of a result of Gromoll and Grove
Urs Frauenfelder, Christian Lange, Stefan Suhr
The theorem that if all geodesics of a Riemannian two-sphere are closed they are also simple closed is generalized to real Hamiltonian structures on . For reversible…
On metrics on 2-orbifolds all of whose geodesics are closed
Christian Lange
We show that the geodesic period spectrum of a Riemannian 2-orbifold all of whose geodesics are closed depends, up to a constant, only on its orbifold topology and compute it. In t…