New degeneration phenomenon for infinite-type Riemann surfaces

抄録

Since the Teichmüller 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, by constructing a concrete example, we prove that if R is a Riemann surface of infinite type, then there exists a Riemann surface with a marking on the Bers boundary that is homeomorphic to the surface R. We also show that such points form an infinite-dimensional complex manifold on the Bers boundary.