Schottky uniformizations of Z22 actions on Riemann surfaces.
Given a closed Riemann surface S together a group of its conformal automorphisms H ≅ Z22, it is known that there are Schottky uniformizations of S realizing H. In this note we proceed to give an explicit Schottky uniformizations for each of all different topological actions of Z22 as group of conformal automorphisms on a closed Riemann surface.
Sector estimates for Kleinian groups.
Sector reflections in the plane.
Self-embeddings of kleinian groups
Sequences and dynamical systems associated with canonical approximation by rationals
Sharp bounds for the intersection of nodal lines with certain curves
Let be a hyperbolic surface and let be a Laplacian eigenfunction having eigenvalue with . Let be the set of nodal lines of . For a fixed analytic curve of finite length, we study the number of intersections between and in terms of . When is compact and a geodesic circle, or when has finite volume and is a closed horocycle, we prove that is “good” in the sense of [TZ]. As a result, we obtain that the number of intersections between and is . This bound is sharp.
Sharp norm estimate of Schwarzian derivative for a class of convex functions
We establish a sharp norm estimate of the Schwarzian derivative for a function in the classes of convex functions introduced by Ma and Minda [Proceedings of the Conference on Complex Analysis, Int. Press, 1992, 157-169]. As applications, we give sharp norm estimates for strongly convex functions of order α, 0 < α < 1, and for uniformly convex functions.
Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form
Simultaneous uniformisation.
Singular sets of holonomy maps for algebraic foliations
In this article we investigate the natural domain of definition of a holonomy map associated to a singular holomorphic foliation of the complex projective plane. We prove that germs of holonomy between algebraic curves can have large sets of singularities for the analytic continuation. In the Riccati context we provide examples with natural boundary and maximal sets of singularities. In the generic case we provide examples having at least a Cantor set of singularities and even a nonempty open set...
Singuläre Eichlerintegrale und verallgemeinerte Eisensteinreihen.
Small spanning sets of cusp forms.
Solution of a combinatorially formulated monodromy problem of Eisenbud and Harris
Some applications of large sieve in Riemann surfaces
Some Curves in Abelian Varieties.
Some examples of discrete groups and hyperbolic orbifolds of infinite volume.
Some loci in Teichmüller space for genus seven defined by vanishing thetanulls.
Some Remarks of Kleinian Groups.
Some remarks on non-discrete Möbius groups.