Construction of Shiba behavior spaces on an open Riemann surface of infinite genus Dedicated to Emeritus Professor Yukio Kusunoki on his 88th birthday

摘要

The concept of behavior spaces introduced by Shiba plays an important role of systematic investigation of abelian differentials on an open Riemann surface. A Shiba behavior space consists of harmonic differentials which satisfy a certain period condition and boundary behavior In this paper, for any open Riemann surface of infinite genus we construct Shiba behavior spaces with arbitrarily prescribed period condition and with specific boundary behavior.