NEW DEGENERATION PHENOMENON FOR INFINITE-TYPE RIEMANN SURFACES
Abstract
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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Analytic and geometric function theory
Publication details
- Journal / source
- Kodai Mathematical Journal
- Volume
- 49
- Issue
- 1
- Pages
- 95–124
- Publication date
- 2 March 2026
- Language
- EN