Abstract
On every compact Riemann surface of genus greater than one, there exist holomorphic differentials and holomorphic quadratic differentials having only simple zeros. The usefulness of such differentials in Teichmüller Theory is well known (cf. L. Ahlfors [1], L. Bers [2]).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ahlfors, L., The complex analytic structure of the space of closed Riemann surfaces, in “Analytic functions”, pp. 45–66, Princeton Univ. Press, Princeton, 1960.
Bers, L., Holomorphic differentials as functions of moduli, Bull. Amer. Math. Soc. 67 (1960), 206–210.
Kusunoki, Y., Beiträge zur Theorie der analytischen Differentiale und Funktionen, Ködai Math. Sem. Rep. 26 (1975), 446–453.
Nevanlinna, R., “Uniformisierung,” Springer Verlag, Berlin Heidelberg New York, 2nd ed., 1967.
Virtanen, K.I., Über Extremalfunktionen auf offenen Riemannschen Flächen, Ann. Acad. Sci. Fenn. Ser. A.I., No. 141 (1952) 7 pp.
Yosida, K., “Functional analysis,” Springer Verlag, 2nd ed., 1968.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag New York Inc.
About this paper
Cite this paper
Kusunoki, Y. (1988). Integrable holomorphic quadratic differentials with simple zeros. In: Drasin, D., Kra, I., Earle, C.J., Marden, A., Gehring, F.W. (eds) Holomorphic Functions and Moduli I. Mathematical Sciences Research Institute Publications, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9602-4_19
Download citation
DOI: https://doi.org/10.1007/978-1-4613-9602-4_19
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-9604-8
Online ISBN: 978-1-4613-9602-4
eBook Packages: Springer Book Archive