Insecurity for compact surfaces of positive genus (2009)
Bangert, Victor, Gutkin, Eugene
A pair of points in a riemannian manifold $M$ is secure if the geodesics between the points can be blocked by a finite number of point obstacles; otherwise the pair of points is insecure. A manifold...
Victor Bangert, Mikhail G. Katz, Steven Shnider
Abstract. We study optimal curvature-free inequalities of the type discovered by C. Loewner and M. Gromov, using a generalisation of the Wirtinger inequality for the comass. Using a model for the...
Secure two-dimensional tori are flat (2008)
Bangert, Victor, Gutkin, Eugene
A riemannian manifold is secure if the geodesics between any pair of points in the manifold can be blocked by a finite number of point obstacles. Compact, flat manifolds are secure. A standing...
The existence of two closed geodesics on every Finsler 2-sphere (2007)
In this paper, we prove that for every Finsler metric on the 2-dimensional sphere there exist at least two distinct prime closed geodesics. For the case of the two-sphere, this solves an open problem...
E_7, Wirtinger inequalities, Cayley 4-form, and homotopy (2006)
Bangert, Victor, Katz, Mikhail G., Shnider, Steven, Weinberger, Shmuel
We study optimal curvature-free inequalities of the type discovered by C. Loewner and M. Gromov, using a generalisation of the Wirtinger inequality for the comass. Using a model for the classifying...
Differentiability of the stable norm in codimension one (2006)
Auer, Franz., Bangert, Victor.
American Journal of Mathematics - Volume 128, Number 1, February 2006
An Optimal Loewner-type Systolic Inequality and Harmonic One-forms of Constant Norm (2004)
Bangert , Victor, Katz , Mikhail
We present a new optimal systolic inequality for a closed Riemannian manifold X, which generalizes a number of earlier inequalities, including that of C. Loewner. We characterize the boundary case of...
Boundary case of equality in optimal Loewner-type inequalities (2004)
Bangert, Victor, Croke, Christopher, Ivanov, Sergei V., Katz, Mikhail G.
We prove certain optimal systolic inequalities for a closed Riemannian manifold (X,g), depending on a pair of parameters, n and b. Here n is the dimension of X, while b is its first Betti number. The...
Filling area conjecture and ovalless real hyperelliptic surfaces (2004)
Bangert, Victor, Croke, Christopher, Ivanov, Sergei V., Katz, Mikhail G.
We prove the filling area conjecture in the hyperelliptic case. In particular, we establish the conjecture for all genus 1 fillings of the circle, extending P. Pu's result in genus 0. We translate...
Differentiability of the stable norm in codimension one (2004)
The real homology of a compact, n-dimensional Riemannian manifold M is naturally endowed with the stable norm. The stable norm of a homology class is the minimal Riemannian volume of its...
An optimal Loewner-type systolic inequality and harmonic one-forms of constant norm (2003)
Bangert, Victor, Katz, Mikhail
We present a new optimal systolic inequality for a closed Riemannian manifold X, which generalizes a number of earlier inequalities, including that of C. Loewner. We characterize the boundary case of...
Stable systolic inequalities and cohomology products (2002)
Bangert, Victor, Katz, Mikhail
Multiplicative relations in the cohomology ring of a manifold impose constraints upon its stable systoles. Given a compact Riemannian manifold (X,g), its real homology H_*(X,R) is naturally endowed...
Closed geodesics on complete surfaces. (1979)
Freiburg (Breisgau), Univ., Habil.-Schr., 1980 (Nicht für den Austausch).
Konvexität in riemannschen Mannigfaltigkeiten / (1977)
Thesis (doctoral)--Universität Dortmund, 1977.