Related papers: New constructions of biharmonic polynomial maps be…
We characterize all possible relative positions between a hyperboloid of one sheet and a sphere through the roots of a characteristic polynomial associated to these quadrics. The classification is also suitable for a hyperboloid and a…
We introduce several homotopy equivalence relations for proper holomorphic mappings between balls. We provide examples showing that the degree of a rational proper mapping between balls (in positive codimension) is not a homotopy invariant.…
In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion.…
The paper is devoted to the study of compositions of polyharmonic mappings in simply connected domains. More precisely, we determine necessary and sufficient conditions of polyharmonic mapping $f$ such that $f\circ F$ (resp. $F\circ f$) is…
In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the…
We compute the monoid of essential self-maps of of the product of two n-spheres fixing the diagonal. More generally, we consider products S x S, where S is a suspension. Essential self-maps of S x S demonstrate the interplay between the…
We study locally harmonic maps between a Riemann surface or Lorentz surface $M$ and a Riemann surface or Lorentz surface $N$. {All four cases are studied in a unified way}. All four cases are written using a unified formalism. Therefore…
We construct CW spheres from the lattices that arise as the closed sets of a convex closure, the meet-distributive lattices. These spheres are nearly polytopal, in the sense that their barycentric subdivisions are simplicial polytopes. The…
We already saw in [A1] that the space of dynamically marked rational maps can be identified to a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In the…
Obtaining constraints from the largest scales of a galaxy survey is challenging due to the survey mask allowing only partial measurement of large angular modes. This scatters information from the harmonic-space 2-point function away from…
In this article, we study holomorphic isometric embeddings between bounded symmetric domains. In particular, we show the total geodesy of any holomorphic isometric embedding between reducible bounded symmetric domains with the same rank.
We introduce two new algebraic invariants, the (co)homological distances between continuous maps, which provide computable lower bounds for the homotopic distance and strictly refine the classical cup-length estimates. We then define the…
We introduce two classes of homogeneous polynomials and show their role in constructing of integrable hierarchies for some integrable lattices.
The aim of these lectures is the study of bifurcations within holomorphic families of polynomials or rational maps by mean of ergodic and pluripotential theoretic tools.
Existence of an infinite sequence of harmonic maps between spheres of certain dimensions was proven by Bizon and Chmaj. This sequence shares many features of the Bartnik-McKinnon sequence of solutions to the Einstein-Yang-Mills equations as…
We construct sense-preserving univalent harmonic mappings which map the unit disk onto a domain which is convex in the horizontal direction, but with varying dilatation. Also, we obtain minimal surfaces associated with such harmonic…
We introduce the notion of locally consistent system of half-spaces for a real hyperplane arrangement. We embed a sphere in the complexified complement by shifting the real unit sphere into the imaginary direction indicated by the…
We give necessary and sufficient conditions for Riemannian maps to be biharmonic. We also define pseudo umbilical Riemannian maps as a generalization of pseudo-umbilical submanifolds and show that such Riemannian maps put some restrictions…
In this paper we analyze some relationships between the topological complexity of a space $X$ and the category of $C_{\Delta_X},$ the homotopy cofibre of the diagonal map $\Delta_X:X\rightarrow X\times X.$ We establish the equality of the…
For $L \hookrightarrow X$ a Lagrangian embedding associated with a real homogeneous space, we construct the moduli space of stable holomorphic discs mapping to $(X,L)$ as an orbifold with corners equipped with a group action. Some essential…