BIMSA >
微分几何讨论班
微分几何讨论班
Asymptotically geodesic hypersurfaces and the fundamental groups of hyperbolic manifolds
Asymptotically geodesic hypersurfaces and the fundamental groups of hyperbolic manifolds
演讲者
韩肖垄
时间
2026年04月28日 14:30 至 16:30
地点
A3-4-301
线上
Zoom 293 812 9202
(BIMSA)
摘要
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.