28 apr 2016 -- 14:30
Sala Seminari, Dipartimento di Matematica, Pisa
Abstract.
It is well known, but not well shown, how to replace a cusp of an hyperbolic Riemann surface with an asymptotically hyperbolic end. We will see a simple proof of this fact using analytical and geometrical tools, without going into detail but keeping a mere exposure. As a corollary we'll be able to glue two hyperbolic Riemann surfaces with cusps obtaining a compact hyperbolic surface whose metric is 'arbitrarily close' to the two starting metrics. It's enough to know the basic definitions of Riemann surface and hyperbolic metric in order to understand this talk. The knowledge of weighted Holder spaces even if it is not strictly required, may help too.