Year: 2026
Type: preprint
Abstract: We give a short proof of the following extension of a recent result of Gadre, Maher, Pfaff and Uyanki: Consider a closed hyperbolic 3-manifold M which fibers over the circle, with fiber a closed surface S. Any measure class on the ideal boundary of hyperbolic 3-space which is invariant and totally ergodic under the action of the fundamental group of M is singular with respect to the push-forward by a Cannon-Thurston map of a stationary measure on the circle of a random walk with finite first moment on the fundamental group of S.
Source: arXiv (Cornell University)
Author: Hamenstaedt, Ursula
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214069151