Convexity of length functions and Fenchel-Nielsen coordinates (joint EGG/Geometry seminar)

Juan Souto, 5 juin 2008, 14h15, MA12.

Abstract:

Kerckhoff and Wolpert proved that the length functions are convex on Teichmueller space with respect to earthquake paths and Weil-Peterson geodesics respectively. The goal of this talk is to prove that they are also convex with respect to suitably chosen Fenchel-Nielsen coordinates. The proof is of synthetic nature. This is joint work with Mladen Bestvina, Ken Bromberg and Koji Fujiwara.