Related papers: Foliations associated to harmonic maps and some co…
The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical…
The idea of transversality is explored in the construction of cohomology theory associated to regularized sequences of multiple products of rational functions associated to vertex algebra cohomology of codimension one foliations on complex…
This chapter is devoted to the analysis of jamming and percolation behavior of two-dimensional systems of elongated particles. We consider both continuous and discrete spaces (with the special attention to the square lattice), as well the…
We study non-compact surfaces obtained by gluing strips $\mathbb{R}\times(-1,1)$ with at most countably many boundary intervals along some these intervals. Every such strip possesses a foliation by parallel lines, which gives a foliation on…
We study harmonic map sequences from surfaces to compact homogeneous spaces. For sequences developing a single bubble, we derive refined asymptotic expansions in the neck region and prove new obstruction relations among the leading…
The questions of global topological, smooth and holomorphic classifications of the differential systems, defined by covering foliations, are considered. The received results are applied to nonautonomous linear differential systems and…
The elegant properties of conformal mappings, when applied to two dimensional (2D) lattices, find interesting applications in 2D foams and other cellular or close packed structures. In particular the 2D honeycomb (whose dual is the…
We study a relationship between rational proper maps of balls in different dimensions and strongly plurisubharmonic exhaustion functions of the unit ball induced by such maps. Putting the unique critical point of this exhaustion function at…
This paper introduces the foliage partition, an easy-to-compute LC-invariant for graph states, of computational complexity $\mathcal{O}(n^3)$ in the number of qubits. Inspired by the foliage of a graph, our invariant has a natural graphical…
The present paper has a number of distinct purposes. First is to give a description of a class of electromagnetic knots from the perspective of foliation theory. Knotted solutions are then interpreted in terms of two codimension-2…
This article is devoted to the geometric construction which states a natural correspondence between topological coverings of a foliated manifolds and noncommutative coverings of the operator algebras. However this correspondence is not one…
Consider the Hamiltonian action of a compact connected Lie group on a transversely symplectic foliation which satisfies the transverse hard Lefschetz property. We establish an equivariant formality theorem and an equivariant symplectic…
We give a geometric characterization of flag geometries associated to Hitchin representations in $\text{SL}_3(\mathbb{R})$. Our characterization is based on distinguished invariant foliations, similar to those studied by Guichard-Wienhard…
We study varieties of complexes of projective modules with fixed ranks, and relate these varieties to the varieties of their homologies. We show that for an algebra of global dimension at most two, these two varieties are related by a pair…
We consider a two dimensional extension of the so-called linearizable mappings. In particular, we start from the Heideman-Hogan recurrence, which is known as one of the linearizable Somos-like recurrences, and introduce one of its two…
We study the topology of the space of smooth codimension one foliations on a closed 3-manifold. We regard this space as the space of integrable plane fields included in the space of all smooth plane fields. It has been known since the late…
We prove that any smooth foliation that admits a Riemannian foliation structure has a well-defined basic signature, and this geometrically defined invariant is actually a foliated homotopy invariant. We also show that foliated homotopic…
Deformation of morphisms along leaves of foliations define the tangential foliation on the corresponding space of morphisms. We prove that codimension one fo-liations having a tangential foliation with at least one non-algebraic leaf are…
Some curvature estimates are derived from geometrical data concerning quasi-conformality properties of some commuting linearly independent vector fields on a compact Riemannian manifold.
We theoretically study the conformations of a helical semi-flexible filament confined to a flat surface. This squeezed helix exhibits a variety of unexpected shapes resembling circles, waves or spirals depending on the material parameters.…