Related papers: Riemann Surface Laminations with Singularities

We survey some recent developments in the ergodic theory for hyperbolic Riemann surface laminations. The emphasis is on singular holomorphic foliations. These results not only illustrate the strong similarity between the ergodic theory of…

This report discusses recent results as well as new perspectives in the ergodic theory for Riemann surface laminations, with an emphasis on singular holomorphic foliations by curves. The central notions of these developments are leafwise…

Let F be a holomorphic foliation of P^2 by Riemann surfaces. Assume all the singular points of F are hyperbolic. If F has no algebraic leaf, then there is a unique positive harmonic $(1,1)$ current $T$ of mass one, directed by F. This…

In this paper, we construct various examples of holomorphic laminations, with leaves of dimension 1, and we also study some of their dynamical properties. In particular we study existence and uniqueness of positive closed currents. We…

Let $\mathcal{L}$ be a Lipschitz lamination by Riemann surfaces embedded in $M$. If $M$ is a complex torus, $\mathbb{CP}^1\times\mathbb{CP}^1$ or $\mathbb{T}^1\times\mathbb{CP}^1$ and there is no directed closed current then there exists a…

If $\mathcal{L}$ is a laminations with hyperbolic singularities, embedded in a compact homogeneous K\"ahler surface, without directed closed positive currents. Then, $\mathcal{L}$ has a unique directed positive harmonic current of mass one.…

We study conformal structure and topology of leaves of singular foliations by Riemann surfaces.

In this paper, we develop $L^2$ theory for Riemannian and Hermitian foliations on manifolds with basic boundary. We establish a decomposition theorem, various vanishing theorems, a twisted duality theorem for basic cohomologies and an…

We show that every topological surface lamination of a 3-manifold M is isotopic to one with smoothly immersed leaves. This carries out a project proposed by Gabai in [Problems in foliations and laminations, AMS/IP Stud. Adv. Math. 2.2…

In this article we survey recent developments in the theory of constant mean curvature surfaces in homogeneous 3-manifolds, as well as some related aspects on existence and descriptive results for $H$-laminations and CMC foliations of…

In this paper we study singular riemannian foliations that have sections,i.e., totally geodesic complete immersed submanifolds that meet each leaf orthogonally and whose dimensions are the codimensions of the regular leaves. We prove here…

Consider a foliation in the projective plane admitting a projective line as the unique invariant algebraic curve. Assume that the foliation is generic in the sense that its singular points are hyperbolic. We show that there is a unique…

In this paper we review some author's results about singular holonomy of singular riemannian foliations with sections (s.r.f.s for short) and also some results of a joint work with Toeben and a joint work with Gorodski. We stress here that…

For a singular Riemannian foliation whose leaves are properly embedded, we show in the first part of this article the existence of global tubular neighbourhoods, and we develop a global description of the foliation as stratification by…

We study the holonomy cocycle H of a holomorphic foliation \Fc by Riemann surfaces defined on a compact complex projective surface X satisfying the following two conditions: 1) its singularities E are all hyperbolic; 2) there is no…

We study local positive harmonic currents directed by a foliation by Riemann surfaces near a hyperbolic singularity which have no mass on the separatrices. A theorem of Nguy\^en says that the Lelong number of such a current at the singular…

We give an easy example showing that sections of a singular Riemannian foliation on a simply connected space neither have to be isometric nor injectively immersed.

We give a new proof of the uniformization theorem of the leaves of a lamination by surfaces of hyperbolic conformal type. We use a laminated version of the Ricci flow to prove the existence of a laminated Riemannian metric (smooth on the…

A smooth foliation is Riemannian when its leaves are locally equidistant. The closures of the leaves of a Riemannian foliation on a simply connected manifold, or more generally of a Killing foliation, are described by flows of transverse…

We construct minimal laminations by hyperbolic surfaces whose generic leaf is a disk and contain any prescribed family of surfaces and with a precise control of the topologies of the surfaces that appear. The laminations are constructed via…