Abstract In this note we discuss the problem of finding an upper bound on the length of the shortest closed geodesic in a closed Riemannian 3-manifold in terms of the volume. More precisely, we show ...
We show that the Hayman-Wu constant $\emptyset$ is strictly smaller than 4Ď€. Previously it has been shown that $\pi^2 \leq \emptyset 4 \pi$. A main tool in our proof is an analysis of the hyperbolic ...
Riemannian manifolds or geodesic metric spaces of finite or infinite dimension occur in many areas of mathematics. We are interested in the interplay between their local geometry and global ...
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