16 citations · 70 across the 19 of their papers we have counts for
26 papers
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…
On the local maximizers of higher capacity ratios
Luca Baracco, Olga Bernardi, Christian Lange +1
We prove an analogue of the 4-dimensional local Viterbo conjecture for the higher Ekeland-Hofer capacities: on the space of 4-dimensional smooth star-shaped domains of unitary volu…
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…
Higher systolic inequalities for 3-dimensional contact manifolds
Alberto Abbondandolo, Christian Lange, Marco Mazzucchelli
A contact form is called Besse when the associated Reeb flow is periodic. We prove that Besse contact forms on closed connected 3-manifolds are the local maximizers of suitable hig…
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…
Seifert fibrations of lens spaces over non-orientable bases
Hansjörg Geiges, Christian Lange
We classify the Seifert fibrations of lens spaces where the base orbifold is non-orientable. This is an addendum to our earlier paper `Seifert fibrations of lens spaces'. We correc…
A Boothby-Wang theorem for Besse contact manifolds
Marc Kegel, Christian Lange
A Reeb flow on a contact manifold is called Besse if all its orbits are periodic, possibly with different periods. We characterize contact manifolds whose Reeb flows are Besse as p…
On the rigidity of Zoll magnetic systems on surfaces
Luca Asselle, Christian Lange
In this paper we study rigidity aspects of Zoll magnetic systems on closed surfaces. We characterize magnetic systems on surfaces of positive genus given by constant curvature metr…
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…
A diameter gap for quotients of the unit sphere
Claudio Gorodski, Christian Lange, Alexander Lytchak +1
We prove that for any isometric action of a group on a unit sphere of dimension larger than one, the quotient space has diameter zero or larger than a universal dimension-independe…
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.
Affine functions on Alexandrov spaces
Christian Lange, Stephan Stadler
We show that every finite-dimensional Alexandrov space X with curvature bounded from below embeds canonically into a product of an Alexandrov space with the same curvature bound an…
Seifert fibrations of lens spaces
Hansjörg Geiges, Christian Lange
We classify the Seifert fibrations of any given lens space L(p,q). We give an algorithmic construction of a Seifert fibration of L(p,q) over the base orbifold S^2(m,n) with the cop…
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…
Classification of finite groups generated by reflections and rotations
Christian Lange, Marina A. Mikhailova
We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has cod…
When is the underlying space of an orbifold a manifold with boundary?
Christian Lange
We answer the question of when the underlying space of an orbifold is a manifold with boundary in several categories.
Characterization of finite groups generated by reflections and rotations
Christian Lange
We characterize finite groups G generated by orthogonal transformations in a finite-dimensional Euclidean space V whose fixed point subspace has codimension one or two in terms of…