## A lower bound for dilatations of certain class of pseudo-Anosov maps of Riemann surfaces

J. Math. Sci. Univ. Tokyo
Vol. 16 (2009), No. 3, Page 441--460.

Zhang, C.
A lower bound for dilatations of certain class of pseudo-Anosov maps of Riemann surfaces
Let $S$ be a Riemann surface of type $(p,n)$ with $3p+n>4$ that contains at least one puncture $a$. Let $\mathscr{S}_{p,n}$ denote the set of pseudo-Anosov maps of $S$ that are isotopic to products of two Dehn twists and are isotopic to the identity map on $\tilde{S}=S\cup \{a\}$. In this article, we give a lower bound for dilatations of elements of $\mathscr{S}_{p,n}$. We also estimate for any hyperbolic structure of $\tilde{S}$ the hyperbolic lengths of those filling closed geodesics of $\tilde{S}$ stemming from the elements of $\mathscr{S}_{p,n}$.