Self-welding continuations of finite open Riemann surfaces

Abstract

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 (R₀) of marked closed Riemann surfaces of positive genus into which a given marked finite open Riemann surface R₀ of the same genus can be conformally embedded. We characterize its boundary (R₀) in terms of self-welding closings of R₀.