A characterization of short curves of a Teichmüller geodesic.
A construction of the Deligne-Mumford orbifold
A foliation of Teichmüller space by twist invariant disks.
A generalisation of Teichmüller space in the hermitian context
A Modular Group and Riemann Surfaces of Genus 2.
A natural graded Lie algebra sheaf over Riemann surfaces
A note on geodesics in infinite-dimensional Teichmüller spaces.
A pseudo-trigonometry related to Ptolemy's theorem and the hyperbolic geometry of punctured spheres
A hyperbolic geodesic joining two punctures on a Riemann surface has infinite length. To obtain a useful distance-like quantity we define a finite pseudo-length of such a geodesic in terms of the hyperbolic length of its surrounding geodesic loop. There is a well defined angle between two geodesics meeting at a puncture, and our pseudo-trigonometry connects these angles with pseudo-lengths. We state and prove a theorem resembling Ptolemy's classical theorem on cyclic quadrilaterals and three general...
A reduction for asymptotic Teichmüller spaces.
A rigidity theorem for Möbius groups.
Action of the Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups in genus zero
In this paper we establish the action of the Grothendieck-Teichmüller group on the prime order torsion elements of the profinite fundamental group . As an intermediate result, we prove that the conjugacy classes of prime order torsion of are exactly the discrete prime order ones of the .
Addendum to: A foliation of Teichmüller space by twist invariant disks.
Affine coordinates for Teichmüller spaces.
Almost complex principal fiber bundles and the complex structure on Teichmüller space.
An algorithm for finding the Veech group of an origami.
Approximate roots of pseudo-Anosov diffeomorphisms
The Root Conjecture predicts that every pseudo-Anosov diffeomorphism of a closed surface has Teichmüller approximate th roots for all . In this paper, we replace the Teichmüller topology by the heights-widths topology – that is induced by convergence of tangent quadratic differentials with respect to both the heights and widths functionals – and show that every pseudo-Anosov diffeomorphism of a closed surface has heights-widths approximate th roots for all .
Arc operads and arc algebras.
Automorphismen und Modularraum Galoisscher dreiblättriger Überlagerungen.
Billards rationnels et espaces de Teichmüller
Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves
We survey variations of the Bergman kernel and their asymptotic behaviors at degeneration. For a Legendre family of elliptic curves, the curvature form of the relative Bergman kernel metric is equal to the Poincaré metric on ℂ 0,1. The cases of other elliptic curves are either the same or trivial. Two proofs depending on elliptic functions’ special properties and Abelian differentials’ Taylor expansions are discussed, respectively. For a holomorphic family of hyperelliptic nodal or cuspidal curves...