Related papers: Poincar\'e problem for weighted projective foliati…

We present fully polynomial approximation schemes for a broad class of Holant problems with complex edge weights, which we call Holant polynomials. We transform these problems into partition functions of abstract combinatorial structures…

We analyze the weight diagram associated with foliations on the complex projective plane through the Hilbert-Mumford criterion in Geometric Invariant Theory, focusing in particular on invariants such as the algebraic multiplicity and the…

We study foliations of space forms by complete hypersurfaces, under some mild conditions on its higher order mean curvatures. In particular, in Euclidean space we obtain a Bernstein-type theorem for graphs whose mean and scalar curvature do…

The aim of this article is to introduce invariants of oriented, smooth, closed four-manifolds, built using the Floer homology theories defined in two earlier papers (math.SG/0101206 and math.SG/0105202). This four-dimensional theory also…

The phase space of an integrable Hamiltonian system is foliated by invariant tori. For an arbitrary Hamiltonian H such a foliation may not exist, but we can artificially construct one through a parameterised family of surfaces, with the…

We study the invariant theory of singular foliations of the projective plane. Our first main result is that a foliation of degree m>1 is not stable only if it has singularities in dimension 1 or contains an isolated singular point with…

For a weighted quasihomogeneous two dimensional hypersurface singularity, we define a smoothing with unipotent monodromy and an isolated graded normal singularity. We study the natural weighted blow up of both the smoothing and the surface.…

The purpose of this paper is to study transport equations on the unit tangent bundle of closed oriented Riemannian surfaces and to connect these to the transport twistor space of the surface (a complex surface naturally tailored to the…

We determine the all-genus Hodge-Gromov-Witten theory of a smooth hypersurface in weighted projective space defined by a chain or loop polynomial. In particular, we obtain the first genus-zero computation of Gromov-Witten invariants for…

We consider hyperbolic and partially hyperbolic diffeomorphisms on compact manifolds. Associated with invariant foliation of these systems, we define some topological invariants and show certain relationships between these topological…

We present some classical and weighted Poincar\'e inequalities for some one-dimensional probability measures. This work is the one-dimensional counterpart of a recent study achieved by the authors for a class of spherically symmetric…

We derive a relationship between the eigenvalues of the Weyl-Schouten tensor of a conformal representative of the conformal infinity of a hyperbolic Poincar\'e manifold and the principal curvatures on the level sets of its uniquely…

We introduce the notion of an asymptotically Poincar\'e family of surfaces in an end of a quasi-Fuchsian manifold. We show that any such family gives a foliation of an end by asymptotically parallel convex surfaces, and that the asymptotic…

We establish new results on weighted $L^2$ extension of holomorphic top forms with values in a holomorphic line bundle, from a smooth hypersurface cut out by a holomorphic function. The weights we use are determined by certain functions…

We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some…

We discuss criteria for the nonexistence, existence and computation of invariant algebraic surfaces for three-dimensional complex polynomial vector fields, thus transferring a classical problem of Poincar\'e from dimension two to dimension…

Let $\mathcal F$ be a foliation on a smooth projective surface $S$ over the complex number $\mathbb{C}$. We introduce three birational non-negative invariants $c_1^2(\mathcal F)$, $c_2(\mathcal F)$ and $\chi(\mathcal F)$, called the Chern…

Hypersurfaces embedded in conformal manifolds appear frequently as boundary data in boundary-value problems in cosmology and string theory. Viewed as the non-null conformal infinity of a spacetime, we consider hypersurfaces embedded in a…

We consider closed and orientable immersed hypersurfaces of translational manifolds. Given a vector field on such a hypersurface, we define a perturbation of its Gauss map, which allows us to obtain topological invariants for the immersion…

We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space $\mathscr F_q(r, d)$ of singular foliations of codimension $q$ and degree $d$ on the complex…