New degeneration phenomenon for infinite-type Riemann surfaces

2024/05/07 by Matsuda, Ryo
#Complex Variables (math.CV) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2405.04178

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, 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.

Related

• Maximal cusps are not dense
• Reduced Bers boundaries of Teichmüller spaces
• Teichmüller extremal maps on infinite Riemann surfaces
• The Boundary at Infinity of the Curve Complex and the Relative Teichmüller Space
• Universal degeneration of Riemann surfaces and fibered complex surfaces