Related papers: Regularization and minimization of Haefliger struc…

We give a Chern-Weil map for the Gel'fand-Fuks characteristic classes of Haefliger-singular foliations, those foliations defined by smooth Haefliger structures with dense regular set. Our characteristic map constructs, out of singular…

We prove that a region in a two-dimensional affine subspace of a normed space $V$ has the least 2-dimensional Hausdorff measure among all compact surfaces with the same boundary. Furthermore, the 2-dimensional Hausdorff area density admits…

Given $X$ a cominuscule Grassmannian (or irreducible Hermitian symmetric space) and an integer $p,$ we compute the minimum $l(p)$ such that $H^0 (\Omega^p_X (l(p)))$ is not 0. This allows us to conclude that any codimension-one foliation of…

We prove that every Kaehler solvmanifold has a finite covering whose holomorphic reduction is a principal bundle. An example is given that illustrates the necessity, in general, of passing to a proper covering. We also answer a stronger…

We construct 4-dimensional Riemannian Lie groups carrying left-invariant conformal foliations with minimal leaves of codimension 2. We show that these foliations are holomorphic with respect to an (integrable) Hermitian structure which is…

We show that the vanishing of the higher dimensional homology groups of a manifold ensures that every almost CR structure of codimension $k$ may be homotoped to a CR structure. This result is proved by adapting a method due to Haefliger…

For a proper immersed minimal disk in $\bf{R}^N$ with quadratic area growth, we show that any harmonic function whose negative part grows at a slow sub-linear rate is constant. This leads to a higher codimensional Bernstein theorem for…

Let $X$ a projective manifold equipped with a codimension $1$ (maybe singular) distribution whose conormal sheaf is assumed to be pseudoeffective. By a theorem of Jean-Pierre Demailly, this distribution is actually integrable and thus…

In 3-dimensional manifolds, we prove that generically in$Diff^1_m(M)$, the existence of a minimal expanding invariant foliation implies stable Bernoulliness.

Bill Thurston proved that taut foliations of hyperbolic 3-manifolds have Euler classes of norm at most one, and conjectured that any integral second cohomology class of norm equal to one is realised as the Euler class of some taut…

Geometric conditions are given so that the leafwise reduced cohomology is of infinite dimension, specially for foliations with dense leaves on closed manifolds. The main new definition involved is the intersection number of subfoliations…

Concerning the problem of classifying complete submanifolds of Euclidean space with codimension two admitting genuine isometric deformations, until now the only known examples with the maximal possible rank four are the real Kaehler minimal…

We classify the hypersurfaces of Euclidean space that carry a totally geodesic foliation with complete leaves of codimension one. In particular, we show that rotation hypersurfaces with complete profiles of codimension one are characterized…

In this article parametric versions of Wilson's plug and Kuperberg's plug are discussed. We show that there is a weak homotopy equivalence induced by the inclusion between the space of non-singular vector fields tangent to a foliation and…

In this article, we prove that a free divisor in a three dimensional complex manifold must be Euler homogeneous in a strong sense if the cohomology of its complement is the hypercohomology of its logarithmic differential forms. F.J.…

Let $X$ be a connected non-compact $2$-dimensional manifold possibly with boundary and $\Delta$ be a foliation on $X$ such that each leaf $\omega\in\Delta$ is homeomorphic to $\mathbb{R}$ and has a trivially foliated neighborhood. Such…

This is a survey article, with essentially complete proofs, of a series of recent results concerning the geometry of the characteristic foliation on smooth divisors in compact hyperk\"ahler manifolds, starting with work by Hwang-Viehweg,…

For an oriented irreducible 3-manifold M with non-empty toroidal boundary, we describe how sutured Floer homology ($SFH$) can be used to determine all fibered classes in $H^1(M)$. Furthermore, we show that the $SFH$ of a balanced sutured…

We study the properties of topological spaces $(X,\tau)$, where $X$ is a definable set in an o-minimal structure and the topology $\tau$ on $X$ has a basis that is (uniformly) definable. Examples of such spaces include the canonical…

Moser's Bernstein theorem \cite{moser61} says that an entire minimal graph of codimension 1 with bounded slope must be a hyperplane. An analogous result for arbitrary codimension is not true, by an example of Lawson-Osserman. Here, we show…