A criterion for the existence of a flat connection on a parabolic vector bundle.
A foliation of Teichmüller space by twist invariant disks.
Addendum to: A foliation of Teichmüller space by twist invariant disks.
Amenable coverings of complex manifolds and holomorphic probalitiy measures.
An extremal problem for harmonic measure.
Analytic Self-Mapping Reducing to the Identity Mapping
Bases for qualitativ differentials.
Basis of homology adapted to the trigonal automorphism of a Riemann surface.
A closed (compact without boundary) Riemann surface S of genus g is said to be trigonal if there is a three sheeted covering (a trigonal morphism) from S to the Riemann sphere, ƒ : S →Ĉ. If there is an automorphism of period three, φ, on S permuting the sheets of the covering, we shall call S cyclic trigonal and will be called trigonal automorphism. In this paper we determine the intersection matrix on the first homology group of a cyclic trigonal Riemann surface on an adapted basis B to the trigonal...
Billards en polygones et groupes fuchsiens
Cannon-Thurston Maps, i-bounded Geometry and a Theorem of McMullen
The notion of i-bounded geometry generalises simultaneously bounded geometry and the geometry of punctured torus Kleinian groups. We show that the limit set of a surface Kleinian group of i-bounded geometry is locally connected by constructing a natural Cannon-Thurston map.
Canonical curves and quadrics of rank 4
Classification of complete minimal surfaces in R3 with total curvature 12... .
Connected components of the strata of the moduli spaces of quadratic differentials
In two fundamental classical papers, Masur [14] and Veech [21] have independently proved that the Teichmüller geodesic flow acts ergodically on each connected component of each stratum of the moduli space of quadratic differentials. It is therefore interesting to have a classification of the ergodic components. Veech has proved that these strata are not necessarily connected. In a recent work [8], Kontsevich and Zorich have completely classified the components in the particular case where the quadratic...
Détermination du nombre des intégrales abéliennes de première espèce
Die Zerlegungscharaktere abelscher total reeller Erweiterungen reeller Funktionenkörper einer Variablen.
Differentials of the second kind for families of Mumford curves
Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices
Let be a flat surface of genus with cone type singularities. Given a bipartite graph isoradially embedded in , we define discrete analogs of the Dirac operators on . These discrete objects are then shown to converge to the continuous ones, in some appropriate sense. Finally, we obtain necessary and sufficient conditions on the pair for these discrete Dirac operators to be Kasteleyn matrices of the graph . As a consequence, if these conditions are met, the partition function of the dimer...
Einige Bemerkungen zum Weierstraßschen Lückensatz.
Erratum: Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards. Invent. Math. 97, 553-583 (1989).
Étude des intégrales abéliennes de troisième espèce