Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-17T04:40:05.604Z Has data issue: false hasContentIssue false

Singular Sets of Some Kleinian Groups

Published online by Cambridge University Press:  22 January 2016

Tohru Akaza*
Affiliation:
Mathematical Institute, Kanazawa University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In our paper Cl] we showed that there exist Schottky groups whose singular sets have positive 1-dimensional measure. Since the example was very complicated, it is natural to seek for simpler examples. Further the problem how about the singular sets of more general groups occurs.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Akaza, T., Poincaré theta-series and singular sets of Schottky groups. Nagoya Math. Jour. 24 (1964), 4365.Google Scholar
[2] Ford, L. R., Automorphic Functions. 2nd Ed. Chelsea (1951).Google Scholar
[3] Myrberg, P. J., Zur Theorie der Konvergenz der Poincaréschen Reihen. Ann. Acad. Sci. Fennicae, (A) 9, No. 4 (1916), 175.Google Scholar
[4] Myrberg, P. J., Die Kapazität der singulären Menge der linearen Gruppen. Ann. Acad. Sci. Fennicae, A. I. 10 (1941), 119.Google Scholar
[5] Petersson, H., Über den Bereich absoluter Konvergenz der Poincaré’schen Reihen. Acta Math. 80 (1948), 2349.Google Scholar
[6] Sario, L., Über Riemannsche Flächen mit hebbarem Rand. Ann. Acad. Sci. Fennicae, A. E. 50 (1948), 179.Google Scholar
[7] Schottky, F., Über eine specialle Function, welche bei einer bestimmten linearen Transformation ihres Arguments unverädert bleibt. Crelle’s Jour. 101 (1887), 227272.Google Scholar