Geodesic cycles and the Weil representation I ; quotients of hyperbolic space and Siegel modular forms
We characterize affine mappings on the unit disk and on rectangles by module conditions. The main result generalizes the classic Schwarz lemma. As an application, we give a sufficient condition for a K-quasiconformal mapping on a Riemann surface to be a Teichmüller mapping.
We give some characterizations for certain homeomorphisms between disks in the complex plane, and we prove some Schwarz type theorems for such homeomorphisms. Our results replace the main result of Chen [Studia Math. 157 (2003)] which we show to be false.
In the present paper, we investigate certain geometric properties and inequalities for the Wright function and mention a few important consequences of our main results. A nonlinear differential equation involving the Wright function is also investigated.
We provide a geometric rigidity estimate à la Friesecke-James-Müller for conformal matrices. Namely, we replace by an arbitrary compact set of conformal matrices, bounded away from and invariant under , and rigid motions by Möbius transformations.
We study polynomial iterative roots of polynomials and describe the locus of complex polynomials of degree 4 admitting a polynomial iterative square root.