We prove that a partial measured foliation of any Riemann surface is realized (in the homotopy) by the horizontal foliation of a unique finite-area holomorphic quadratic differential iff it has a finite Dirichlet integral. We then establish a connection between the space of finite-area holomorphic quadratic differentials and the type of the underlying surface. Finally, we discuss applications to the Teichmuller theory.

Bio: BA in mathematics from University of Belgrade, June 1995. MA in mathematics from University of Belgrade, August 1997. PhD in mathematics from City University of New York, October 2001, advisors Linda Keen and Frederick Gardiner. Post-doctoral appointments: University of Southern California, September 2001-June 2004, mentor Francis Bonahon, and Stony Brook University IMS July 2004-July 2006, mentor Mikhail Lyubich. Visiting position University of Maryland, September 2006- February 2007. Tenured position City University of New York, Queens College, February 2007-current. Rank: Professor, Department of Mathematics.