Linearly growing injectivity radius in negatively curved manifolds with small critical exponent.
Vortrag von Prof. Dr. Ilya Gekhtman
Sprecher eingeladen von: Prof. Dr. Alexander Gorodnik
Datum: 17.09.25 Zeit: 13.30 - 14.30 Raum: Y27H28
Let X be a proper geodesic Gromov hyperbolic space whose isometry group contains a uniform lattice \Gamma.
For instance, X could be a negatively curved contractible manifold or a Cayley graph of a hyperbolic group.
Let H be a discrete subgroup of isometries of X with critical exponent (exponential growth rate) strictly less than half of the growth rate of \Gamma.
We show that the injectivity radius of X/H grows linearly along almost every geodesic in X (with respect to the Patterson-Sullivan measure on the Gromov boundary of X).
The proof will involve an elementary analysis of a novel concept called the "sublinearly horosherical limit set" of H which is a generalization of the classical concept of "horospherical limit set" for Kleinian groups.
This talk is based on joint work with Inhyeok Choi and Keivan Mallahi-Kerai.