Conitinuous leafwise harmonic functions on codimension one transversely isometric foliations

Shape of matchbox manifolds

In this work, we develop shape expansions of minimal matchbox manifolds without holonomy, in terms of branched manifolds formed from their leaves. Our approach is based on the method of coding the holonomy groups for the foliated spaces, to define leafwise regions which are transversely stable and are adapted to the foliation dynamics. Approximations are obtained by collapsing appropriately chosen neighborhoods onto these regions along a "transverse Cantor foliation". The existence of the "transverse Cantor foliation" allows us to generalize standard techniques known for Euclidean and fibered …

Free minimal actions of solvable Lie groups which are not affable

We construct an uncountable family of transversely Cantor laminations of compact spaces defined by free minimal actions of solvable groups, which are not affable and whose orbits are not quasi-isometric to Cayley graphs.

叶状流的迹公式

A trace formula for foliated flows

本文针对闭流形上的余维数1叶状流，通过定义Lefschetz分布并利用b-迹等重整化过程，证明了基于闭轨道与保叶无穷小数据的迹公式，从而解决了C.~Deninger关于两个叶向简约上同调的猜想。

每个非紧曲面都是一个极小叶状结构的叶

Every noncompact surface is a leaf of a minimal foliation

本文证明任意非紧定向曲面均可作为闭3维流形中极小叶状结构的叶，并构造可同时包含可数多种开曲面拓扑的双曲例子。