Related papers: Constructing Strebel differentials via Belyi maps …

We obtain necessary conditions for the existence of special K\"ahler structures with isolated singularities on compact Riemann surfaces. We prove that these conditions are also sufficient in the case of the Riemann sphere and, moreover, we…

We show a method to construct a special Lagrangian submanifold L' from a given special Lagrangian submanifold L in a Calabi-Yau manifold with the use of generalized perpendicular symmetries. We use moment maps of the actions of Lie groups,…

Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials…

Our aim in this paper is to provide a theory of discrete Riemann surfaces based on quadrilateral cellular decompositions of Riemann surfaces together with their complex structure encoded by complex weights. Previous work, in particular of…

Motivated by known examples of Joyce structures on spaces of meromorphic quadratic differentials, we consider the isomonodromic deformations of particular second-order linear ODEs with rational potential. We show the infinitesimal…

The local invariants of a meromorphic Abelian differential on a Riemann surface of genus $g$ are the orders of zeros and poles, and the residues at the poles. The main result of this paper is that with few exceptions, every pattern of…

We give an explicit construction of the Brownian sphere biased by the distance between two distinguished points, which is based on the Miermont bijection for quadrangulations. We then describe various conditionings of this object, which are…

An increasingly important area of interest for mathematicians is the study of Abelian differentials. This growing interest can be attributed to the interdisciplinary role this subject plays in modern mathematics, as various problems of…

We define Strebel differentials for stable complex curves, prove the existence and uniqueness theorem that generalizes Strebel's theorem for smooth curves, prove that Strebel differentials form a continuous family over the moduli space of…

We present an algorithmic way of exactly computing Belyi functions for hypermaps and triangulations in genus 0 or 1, and the associated dessins, based on a numerical iterative approach initialized from a circle packing combined with…

We construct the moduli space of r-jets at a point of Riemannian metrics on a smooth manifold. The construction is closely related to the problem of classification of jet metrics via differential invariants. The moduli space is proved to be…

The present paper shows that for a given integer k greater than 2 it is possible to construct an at least k-differentiable Riemannian metric on the sphere of a certain dimension such that the cut locus of a point of it becomes a fractal.…

The moduli space of charge k SU(2) BPS monopoles is diffeomorphic to the moduli space of degree k rational maps between Riemann spheres. In this note we describe a numerical algorithm to compute the monopole fields and energy density from…

There are some existence problems of Jenkins-Strebel differentials on a Riemann surface. The one of them is to find a Jenkins-Strebel differential whose characteristic ring domains have given positive numbers as their circumferences, for…

We construct non-trivial continuous isospectral deformations of Riemannian metrics on the ball and on the sphere in $\R^n$ for every $n\geq 9$. The metrics on the sphere can be chosen arbitrarily close to the round metric; in particular,…

We establish a correspondence on a Riemann surface between hyperbolic metrics with isolated singularities and bounded projective functions whose Schwarzian derivatives have at most double poles and whose monodromies lie in ${\rm…

We give four applications of Zalcman's lemma to the dynamics of rational maps on the Riemann sphere: a parameter analogue of a proof of the density of repelling cycles in the Julia sets;similarity between the Mandelbrot set and the Julia…

We consider a special scattering experiment with n particles in $\mathbb{R}^{n-3,1}$. The scattering equations in this set-up become the saddle-point equations of a Penner-like matrix model, where in the large $n$ limit, the spectral curve…

We construct a moduli space for Riemann surfaces that is universal in the sense that it represents compact Riemann surfaces of any finite genus. This moduli space is stratifed according to genus, and it carries a metric and a measure that…

In this paper, we derive some new results for the separation of two not necessarily convex cones by a (convex) cone / conical surface in real (reflexive) normed spaces. In essence, we follow the nonlinear and nonsymmetric separation…