Noded Teichmueller spaces

Let $G$ be a finitely generated Kleinian group and let $\mathrm{\Delta }$ be an invariant collection of components in its region of discontinuity. The Teichm"uller space $T(\mathrm{\Delta },G)$ supported in $\mathrm{\Delta }$, is the space of equivalence classes of quasiconformal homeomorphisms with complex dilatation invariant under $G$ and supported in $\mathrm{\Delta }$. In this paper we propose a partial closure of $T(\mathrm{\Delta },G)$ by considering certain deformations of the above homeomorphisms. Such a partial closure is denoted by $NT(\mathrm{\Delta },G)$ and called the {\it noded Teichm"uller space} of $G$ supported in $\mathrm{\Delta }$. Some concrete examples are discussed.