Construction of Shiba behavior spaces on an open Riemann surface of infinite genus

Abstract

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.