Related papers: Separation properties of codimension-1 maps betwee…

We prove a dimension distortion estimate for mappings of sub-exponentially integrable distortion in Euclidean spaces, which is essentially sharp in the plane.

In a previous paper we built a modified Hamiltonian formalism to make possible explicit maps among manifolds. In this paper the modified formalism was generalized. As an application, we have built maps among spaces associated to spinors, as…

We review properties of closed meromorphic $1$-forms and of the foliations defined by them. We present and explain classical results from foliation theory, like index theorems, the existence of separatrices, and resolution of singularities…

We will describe some results regarding the algorithmic nature of homeomorphism problems for manifolds; in particular, the following theorem. Theorem 1: Every PL or smooth simply connected manifold M^n of dimension n at least 5 can be…

We apply the algebraic-geometric techniques developed for the study of mappings which have the singularity confinement property to mappings which are integrable through linearisation. The main difference with respect to the previous studies…

Suppose that the 3-manifold M is given by integral surgery along a link L in S^3. In the following we construct a stable map from M to the plane, whose singular set is canonically oriented. We obtain upper bounds for the minimal numbers of…

In this talk, I will discuss the use of harmonic functions to study the geometry and topology of complete manifolds. In my previous joint work with Luen-fai Tam, we discovered that the number of infinities of a complete manifold can be…

We determine the number of connected components of the moduli space for representations of a surface group in the general linear group.

A generalized numerical semigroup is a submonoid $S$ of $\mathbb{N}^d$ with finite complement in it. We characterize isomorphisms between these monoids in terms of permutation of coordinates. Considering the equivalence relation that…

We present a boundary integral method for numerical computation of the capacity of generalized condensers. The presented method applies to a wide variety of generalized condenser geometry including the cases when the plates of the…

We propose a new approach, named PolyMapper, to circumvent the conventional pixel-wise segmentation of (aerial) images and predict objects in a vector representation directly. PolyMapper directly extracts the topological map of a city from…

We study the homomorphism induced in homology by a closed correspondence between topological spaces, using projections from the graph of the correspondence to its domain and codomain. We provide assumptions under which the homomorphism…

Generalizing Heegaard splittings of 3-manifolds and trisections of 4-manifolds, we consider multisections of higher-dimensional smooth (or PL) closed orientable manifolds, namely decompositions into 1-handlebodies whose subcollections…

This paper points out the usefulness of the concept of derivation along a map in many problems in Geometry and Physics. In particular it will be shown that this approach allows us to translate the usual concepts arising in Geometrical…

We consider the problem of computing the distance-dependent two-point function of general planar maps and hypermaps, i.e. the problem of counting such maps with two marked points at a prescribed distance. The maps considered here may have…

A smooth map between manifolds is said to be \emph{image simple} if its restriction to its singular point set is a topological embedding. We study the parity of the number of connected components of the singular point set for image simple…

For a multi-component system, general formulas are derived for the dimension of a coexisting region in the phase diagram in various state spaces.

The boundedness tests for the number of compact integral manifolds of autonomous ordinary differential systems, of autonomous total differential systems, of linear systems of partial differential equations, of Pfaff systems of equations,…

Using the adjoint action of the infinitesimal translations (with respect to some (in)dependant variables) on specific finite-dimensional subspaces of the space of generalized symmetries of some system of partial differential equations, we…

We present a new systematic method to construct the conformal mapping from outside the unit disc to outside of a simply connected domain using the generalized polarization tensors. We also present some numerical results to validate…