We prove a new classification result for (CR) rational maps from the unit sphere in some ${mathbb C}^n$ to the unit sphere in ${mathbb C}^N$. To so so, we work at the level of Hermitian forms, and we introduce ancestors and descendants.
We develop a link between degree estimates for rational sphere maps and compressed sensing. We provide several new ideas and many examples, both old and new, that amplify connections with linear programming. We close with a list of ten open problems.
We prove that under mild hypothesis rational maps on a surface preserving webs are of Latt`es type. We classify endomorphisms of P^2 preserving webs, extending former results of Dabija-Jonsson.
In this manuscript, by using Belyi maps and dessin denfants, we construct some concrete examples of Strebel differentials with four double poles on the Riemann sphere. As an application, we could give some explicit cone spherical metrics on the Riemann sphere.
An argument is given to associate integrable nonintegrable transition of discrete maps with the transition of Lawveres fixed point theorem to its own contrapositive. We show that the classical description of nonlinear maps is neither complete nor totally predictable.
With the sphere $mathbb{S}^2 subset mathbb{R}^3$ as a conductor holding a unit charge with logarithmic interactions, we consider the problem of determining the support of the equilibrium measure in the presence of an external field consisting of finitely many point charges on the surface of the sphere. We determine that for any such configuration, the complement of the equilibrium support is the stereographic preimage from the plane of a union of classical quadrature domains, whose orders sum to the number of point charges.