Subhyperbolic rational maps on boundaries of hyperbolic components

In this paper, we prove that every quasiconformal deformation of a subhyperbolic rational map on the boundary of a hyperbolic component \begin{document}$ \mathcal{H} $\end{document} still lies on \begin{document}$ \partial \mathcal{H} $\end{document} . As an application, we construct geometrically finite rational maps with buried critical points on the boundaries of some hyperbolic components.