Explicit formulae for cocycles of holomorphic vector fields with values in densities.
Extremal Length, Extremal Regions and Quadratic Differentials.
Extremal Quasiconformal Mappings with Free Boundary Components in Domains of Arbitray Connectivity.
Formes automorphes associées aux cycles géodésiques des surfaces de Riemann hyperboliques
Généralisation des fonctions doublement périodiques de seconde espèce
Homology, Belyi functions and canonical curves.
Hyperbolicity of the Complement of Plane Curves.
Hyperelliptic action integral
Applying the “exact WKB method” (cf. Delabaere-Dillinger-Pham) to the stationary one-dimensional Schrödinger equation with polynomial potential, one is led to a multivalued complex action-integral function. This function is a (hyper)elliptic integral; the sheet structure of its Riemann surface above the plane of its values has interesting properties: the projection of its branch-points is in general a dense subset of the plane, and there is a group of symmetries acting on the surface. The distribution...
Measured geodesic laminations in Flatland
Since their introduction by Thurston, measured geodesic laminations on hyperbolic surfaces occur in many contexts. In this survey, we give a generalization of geodesic laminations on surfaces endowed with a half-translation structure (that is a singular flat surface with holonomy ), called flat laminations, and we define transverse measures on flat laminations similar to transverse measures on hyperbolic laminations, taking into account that the images of the leaves of a flat lamination are in...
Natural algebraic representation formulas for curves in ℂ³
We consider several explicit examples of solutions of the differential equation Φ₁’²(z) + Φ₂’²(z) + Φ₃’²(z) = d²(z) of meromorphic curves in ℂ³ with preset infinitesimal arclength function d(z) by nonlinear differential operators of the form (f,h,d) → V(f,h,d), V = (Φ₁,Φ₂,Φ₃), whose arguments are triples consisting of a meromorphic function f, a meromorphic vector field h, and a meromorphic differential 1-form d on an open set U ⊂ ℂ or, more general, on a Riemann surface Σ. Most of them are natural...
Nielsen's theorem and the super-Teichmüller space
Non-Hyperelliptic Weierstrass Points of Maximal Weight.
On a problem of Seiberg and Witten
We describe alternate methods of solution for a model arising in the work of Seiberg and Witten on N = 2 supersymmetric Yang-Mills theory and provide a complete argument for the characterization put forth by Argyres, Faraggi, and Shapere of the curve .
On Analytic Self -Mappings of Riemann Surfaces II.
On Analytic Self-Mappings of Riemann Surfaces.
On first order elliptic equations for sections of complex line bundles
On monodromy map.
On quasiconformal mappings of open Riemann surfaces.
On the Density of Strebel Differentials.
On the determinant of the bundle of meromorphic quadratic differentials on the Deligne-Mumford compactification of the moduli space of Riemann surfaces.