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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.
Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. By using Strebel differentials as a bridge, we construct a new class of cone spherical metrics on compact Ri
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 study the dynamical properties of a large class of rational maps with exactly three ramification points. By constructing families of such maps, we obtain infinitely many conservative maps of degree $d$; this answers a question of Silverman. Rather
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.
Strebel differentials are a special class of quadratic differentials with several applications in string theory. In this note we show that finding Strebel differentials with integral lengths is equivalent to finding generalized Argyres-Douglas singul