Geometrically and topologically random surfaces in a closed hyperbolic three manifold
Geometric Topology
2023-09-07 v1 Differential Geometry
Abstract
We study the distribution of geometrically and topologically nearly geodesic random surfaces in a closed hyperbolic 3-manifold M. In particular, we describe PSL(2,R) invariant measures on the Grassmann bundle G(M) which arise as limits of random minimal surfaces. It is showed that if M contains at least one totally geodesic subsurface then every topological limiting measure is totally scarring (i.e supported on the totally geodesic locus), while we prove that geometrical limiting measures are never totally scarring.
Cite
@article{arxiv.2309.02847,
title = {Geometrically and topologically random surfaces in a closed hyperbolic three manifold},
author = {Jeremy Kahn and Vladimir Markovic and Ilia Smilga},
journal= {arXiv preprint arXiv:2309.02847},
year = {2023}
}
Comments
47 pages, 2 figures