Date:	Tue, March 1, 2016
Time:	14:15
Place:	Research I Seminar Room

Abstract: There are three theorems on existence of quadratic differentials with closed trajectories on a Riemann surface R according to the data which are prescribed. I will prove the version of the existence theorem (due to Hubard-Masur and Renelt) when the heights of the ring domains are prescribed. In this case, the constructed quadratic differential gives a canonical decomposition of the surface R into annuli foliated by the closed trajectories. The result is relevant for extremal length problems on Riemann surfaces and is used in the Dylan Thurston “positive” combinatorial characterisation of rational maps