Variation of the Green function of Riemann surfaces and Whitney's holomorphic stratification conjecture
We classify Veech groups of tame non-compact flat surfaces. In particular we prove that all countable subgroups of ) avoiding the set of mappings of norm less than 1 appear as Veech groups of tame non-compact flat surfaces which are Loch Ness monsters. Conversely, a Veech group of any tame flat surface is either countable, or one of three specific types.
Let σ denote the class of bi-univalent functions f, that is, both f(z) = z + a₂z² + ⋯ and its inverse are analytic and univalent on the unit disk. We consider the classes of strongly bi-close-to-convex functions of order α and of bi-close-to-convex functions of order β, which turn out to be subclasses of σ. We obtain upper bounds for |a₂| and |a₃| for those classes. Moreover, we verify Brannan and Clunie’s conjecture |a₂| ≤ √2 for some of our classes. In addition, we obtain the Fekete-Szegö relation...
On montre que tout point de Misiurewicz dans l’ensemble de Mandelbrot possède un système fondamental de voisinages connexes dans .