2024/11/04 by Masayuki Asaoka, Asaoka, Masayuki, Yushi Nakano +5
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics and Applications #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2411.02106
openalex publication_date 2024/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study geometrical and dynamical properties of codimension one foliations, by exploring a relation between length averages and ball averages of certain group actions. We introduce a new mechanism, which relies on the group structure itself, to obtain irregular behavior of ball averages for certain non-amenable group actions. Several geometric realization results show that any such groups can appear connected with the topology of leaves which are connected sums of plugs with a special geometry, namely nearly equidistant boundary components. This is used to produce the first examples of codimension one \mathcal C^∞ regular foliations on a compact Riemannian manifold M for which the length average of some continuous function does not exist on a non-empty open subset of M.