Consider the problem of estimating the minimum entropy of pseudo-Anosov maps on a surface of genus with punctures. We determine the behavior of this minimum number for a certain large subset of the plane, up to a multiplicative constant. In particular, we show that for fixed , this minimum value behaves as , proving what Penner speculated in 1991.
"Pseudo-Anosov maps with small stretch factors on punctured surfaces." Algebr. Geom. Topol. 20 (4) 2095 - 2128, 2020. https://doi.org/10.2140/agt.2020.20.2095