报告题目: Holomorphic Mappings of Once-holed Tori

报告人：Professor Makoto Masumoto (Yamaguchi University, Japan)

报告时间：8月19日 16:00-17:00

报告地点：1218

摘要：By the general uniformization theorem every Riemann surface of genus zero is
conformally embedded into the Riemann sphere. Thus function theory on such
Riemann surfaces is, in a sense, part of function theory on plane domains.
Therefore the core of theory of Riemann surfaces should be occupied by the
study of Riemann surfaces of positive genus, that is, Riemann surfaces with
handles.

One method for examining the effects of handles in function theory of Riemann
surfaces of positive genus is to develop function theory on once-holed tori. A
once-holed torus is, by denition, a Riemann surface homeomorphic to a torus
with one point removed. Once-holed tori are the simplest among the Riemann
surfaces of positive genus, and are building blocks for Riemann surfaces of
positive genus.

In this talk we address the existence problem of handle-preserving holomorphic
mappings of once-holed tori into a given Riemann surface of positive genus. The
once-holed tori allowing such mappings form a subset of the Teichmueller space
of a once-holed torus. We investigate its geometric properties.

欢迎感兴趣的师生前来参加！