BIMSA >
Differential Geometry Seminar
Differential Geometry Seminar
Asymptotically geodesic hypersurfaces and the fundamental groups of hyperbolic manifolds
Asymptotically geodesic hypersurfaces and the fundamental groups of hyperbolic manifolds
Organizers
Speaker
Xiaolong Han
Time
Tuesday, April 28, 2026 2:30 PM - 4:30 PM
Venue
A3-4-301
Online
Zoom 293 812 9202
(BIMSA)
Abstract
Let M be a closed hyperbolic manifold. A sequence of closed, smoothly immersed hypersurfaces in M (up to homotopy and commensurability) is asymptotically geodesic if they are eventually totally geodesic. We show that if M contains such a sequence, its fundamental group is virtually special and thus a linear group with integer coefficients. If, in addition, M is arithmetic of type I, we build a sequence of asymptotically geodesic, strongly filling hypersurfaces that are equidistributing in the Grassmann bundles, where strongly filling implies a hypersurface having essential intersection with every geodesic.
This partially answers a question of Ben Lowe and Fernando Al Assal regarding the gap of hypersurfaces in higher dimensional hyperbolic manifolds and is a joint work with Ruojing Jiang.
This partially answers a question of Ben Lowe and Fernando Al Assal regarding the gap of hypersurfaces in higher dimensional hyperbolic manifolds and is a joint work with Ruojing Jiang.
Speaker Intro
Xiaolong Han is an Assistant professor at Shanghai Institute of Mathematics and Interdisciplinary Sciences. Before joining SIMIS, he was a postdoc at Yau Mathematica Sciences Center at Tsinghua University. In 2021, he obtained his PhD degree from University of Illinois Urbana-Champaign. His research interest is low-dimensional manifolds and hyperbolic geometry.