New degeneration phenomenon for infinite-type Riemann surfaces

Abstract

Since the Teichm\"uller space of a surface $R$ is a deformation space of complex structures defined on $R$, its Bers boundary describes the degeneration of complex structures in a certain sense. In this paper, constructing a concrete example, we prove that if S is a Riemann surface of infinite type, there exists a Riemann surface with the marking, which is homeomorphic to the surface $R$ in the Bers boundary. We also show that many such degenerations exist in the Bers boundary.