TOTALLY GEODESIC HOMEOMORPHISMS BETWEEN TEICHMULLER SPACES

First, we show that a projective measured foliation is a Busemann point, in Gardiner-Masur boundary, if and only if it is indecomposable. Let f : T-g,T-n -> T-g,T-n be a totally geodesic homeomorphism and suppose that f admits a homeomorphic extension to partial derivative T-GM (g,n). We show that f induces a simplicial automorphism of curve complex. Moreover, the restriction of f on T-g,T-n is an isometry. As an application, we obtain an alternative proof of Royden's Theorem.