Self-welding continuations of finite open Riemann surfaces

We introduce a new kind of welding of compact bordered Riemann surfaces, called a self-welding. We develop its fundamental theory, and apply the results to investigate, in the frame of Teichmüller theory, the set $\mathfrak{M}(\boldsymbol{R}_{0})$ of marked closed Riemann surfaces of positive genus into which a given marked finite open Riemann surface $\boldsymbol{R}_{0}$ of the same genus can be conformally embedded. We characterize its boundary $\partial\mathfrak{M}(\boldsymbol{R}_{0})$ in terms of self-welding closings of $\boldsymbol{R}_{0}$.