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Boundary case of equality in optimal Loewner-type inequalities
Victor Bangert, Christopher Croke, Sergei V. Ivanov +1
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 firs…
Filling area conjecture and ovalless real hyperelliptic surfaces
Victor Bangert, Christopher Croke, Sergei V. Ivanov +1
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…
Differentiability of the stable norm in codimension one
Franz Auer, Victor Bangert
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…