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math.DG2023
A quadratic lower bound for the number of minimal geodesics
Bernd Ammann, Clara Loeh
A minimal geodesic on a Riemannian manifold is a geodesic defined on that lifts to a globally distance minimizing curve on the universal covering. Bangert proved that…
math.GT2023
A roadmap to the (vanishing of the) Euler characteristic
Clara Loeh, George Raptis
We give a diagrammatic summary of the connections between various theorems and conjectures about the vanishing of the Euler characteristic.
math.GR2023
Exponential growth rates in hyperbolic groups (after Koji Fujiwara and Zlil Sela)
Clara Loeh
A classical result of Jørgensen and Thurston shows that the set of volumes of finite volume complete hyperbolic -manifolds is a well-ordered subset of the real numbers of order…