题目: Linearly Growing Injectivity Radius in Negatively Curved Manifolds with Small Critical Exponent

报告人：Assistant Professor Ilya Gekhtman （Technion-Israel Institute of Technology）

时间：2025年3月20日 9:30-10:30

地点：致远楼108室 

摘要: 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, building on joint work with Inhyeok Choi, Wenyuan Yang and Tianyi Zheng.

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