11 citations · 28 across the 13 of their papers we have counts for
14 papers
A Riemannian plane with only two injective Geodesics
Victor Bangert, Stefan Suhr
We present an example of a complete Riemannian plane with precisely two injective geodesics - up to reparameterization. The example arises as a perturbation of a surface of revolut…
An area bound for surfaces in Riemannian manifolds
Victor Bangert, Ernst Kuwert
Let be a compact Riemannian manifold not containing any totally geodesic surface. Our main result shows that then the area of any complete surface immersed into is bounded…
Area growth and rigidity of surfaces without conjugate points
Victor Bangert, Patrick Emmerich
We prove flatness of complete Riemannian planes and cylinders without conjugate points under optimal conditions on the area growth.
On the flatness of Riemannian cylinders without conjugate points
Victor Bangert, Patrick Emmerich
What are appropriate geometric conditions ensuring that a complete Riemannian 2-cylinder without conjugate points is flat? Examples with nonpositive curvature show that one has to…
Isoperimetric Inequalities for Minimal Submanifolds in Riemannian Manifolds: A Counterexample in Higher Codimension
Victor Bangert, Nena Roettgen
For compact Riemannian manifolds with convex boundary, B.White proved the following alternative: Either there is an isoperimetric inequality for minimal hypersurfaces or there exis…
Insecurity for compact surfaces of positive genus
Victor Bangert, Eugene Gutkin
A pair of points in a riemannian manifold is secure if the geodesics between the points can be blocked by a finite number of point obstacles; otherwise the pair of points is in…