## 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
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Abstract:
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 $\mathscr{S}_{p,n}$.

Keywords: Riemann surfaces, pseudo-Anosov, Dehn twists, dilatations, Mapping classes, Teichm\"{u}ller spaces.

Mathematics Subject Classification (2000): Primary 32G15; Secondary 30C60, 30F60
Mathematical Reviews Number: MR2597395