Journal of the Mathematical Society of Japan

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

Kunihiko MATSUI and Fumio MAITANI

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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.

Article information

Source
J. Math. Soc. Japan, Volume 66, Number 2 (2014), 565-580.

Dates
First available in Project Euclid: 23 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1398258184

Digital Object Identifier
doi:10.2969/jmsj/06620565

Mathematical Reviews number (MathSciNet)
MR3201826

Zentralblatt MATH identifier
1291.30240

Subjects
Primary: 30F30: Differentials on Riemann surfaces

Keywords
Riemann surface harmonic differential Shiba behavior space

Citation

MATSUI, Kunihiko; MAITANI, Fumio. Construction of Shiba behavior spaces on an open Riemann surface of infinite genus. J. Math. Soc. Japan 66 (2014), no. 2, 565--580. doi:10.2969/jmsj/06620565. https://projecteuclid.org/euclid.jmsj/1398258184


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References

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