Bounded deviations in higher genus II: minimal laminations

TL;DR

This paper extends the study of bounded deviations in surface homeomorphisms to higher genus surfaces, focusing on minimal laminations beyond closed geodesics, generalizing known results from the torus case.

Contribution

It completes the analysis of bounded deviations for higher genus surfaces by addressing minimal laminations that are not just closed geodesics, broadening the scope of previous work.

Findings

Generalizes bounded deviation results to higher genus surfaces

Analyzes minimal laminations beyond closed geodesics

Completes the theoretical framework initiated in prior work

Abstract

This article follows and completes [arXiv:2511.14222], where we study the problem of bounded deviations for homeomorphisms of closed surfaces of genus $\ge 2$. This second part deals with bounded deviations relative to geodesic minimal laminations that are not reduced to a closed geodesic. The combination of both articles generalises to the higher genus case most of the bounded deviations results already known for the torus.