T. Firsova, M. Lyubich
$\lambda$-Lemma for families of Riemann surfaces and the critical loci of complex Hénon map

We prove a version of the classical $\lambda$-lemma for holomorphic families of Riemann surfaces. We then use it to show that critical loci for complex Hénon maps that are small perturbations of quadratic polynomials with Cantor Julia sets are all quasiconformally equivalent.