Foliations of defined by -actions
In this paper we give a geometric characterization of the 2-dimensional foliations on compact orientable 3-manifolds defined by a locally free smooth action of .
Foliations of surfaces I : an ideal boundary
Let be a foliation of the punctured plane . Any non-compact leaf of has two ends, which we call leaf-ends. The set of leaf-ends which converge to the origin has a natural cyclic order. In the case is infinite, we show that the cyclicly ordered set , obtained by identifying neighbors in and filling in the holes according to the Dedeking process, is equivalent to a circle. We show that the set has a natural topology, and it is homeomorphic to with respect to this topology.
Foliations on the complex projective plane with many parabolic leaves
We prove that a foliation on with hyperbolic singularities and with “many" parabolic leaves (i.e. leaves without Green functions) is in fact a linear foliation. This is done in two steps: first we prove that there exists an algebraic leaf, using the technique of harmonic measures, then we show that the holonomy of this leaf is linearizable, from which the result follows easily.
Foliations transverse to fibers of Seifert manifolds.
Foliations with all leaves compact
The notion of the “volume" of a leaf in a foliated space is defined. If is a compact leaf, then any leaf entering a small neighbourhood of either has a very large volume, or a volume which is approximatively an integral multiple of the volume of . If all leaves are compact there are three related objects to study. Firstly the topology of the quotient space obtained by identifying each leaf to a point ; secondly the holonomy of a leaf ; and thirdly whether the leaves have a locally bounded volume....
Foliations with complex leaves
Let be a smooth foliation with complex leaves and let be the sheaf of germs of smooth functions, holomorphic along the leaves. We study the ringed space . In particular we concentrate on the following two themes: function theory for the algebra and cohomology with values in .
Foliations with few non-compact leaves.
Forme canonique sur le dual du fibré transverse
Formes Différentielles de Degré 1 Fermées Non Singulières: Classes d'Homotopie de leurs Noyaux
Formules pour la multiplicité et le nombre de Milnor d’un feuilletage sur
Generic properties of proper foliations
Geometric expansion, Lyapunov exponents and foliations
Geometrically finite groups, Patterson-Sullivan measures and Ratner's rigidity theorem.
Géométrie des tissus
Geometry and function algebra on pseudo-flat manifolds
Geometry and topology of -covered foliations.
Geometry of Markov systems and codimension one foliations
We show that the theory of graph directed Markov systems can be used to study exceptional minimal sets of some foliated manifolds. A C¹ smooth embedding of a contracting or parabolic Markov system into the holonomy pseudogroup of a codimension one foliation allows us to describe in detail the h-dimensional Hausdorff and packing measures of the intersection of a complete transversal with exceptional minimal sets.
Geometry of the Complex Homogeneous Monge-Ampère Equation.
Group negative curvature for 3-manifolds with genuine laminations.
Growth of leaves.