Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-01-26T03:56:42.521Z Has data issue: false hasContentIssue false
  • English
  • Français

P-harmonic dimensions on ends

Published online by Cambridge University Press:  22 January 2016

Michihiko Kawamura  and
Shigeo Segawa
Michihiko Kawamura
Affiliation:
Department of Mathematics, Faculty of Education, Gifu University, Yanagido, Gifu 501-11, Japan
Shigeo Segawa
Affiliation:
Department of Mathematics, Daido Institute of Technology, Daido, Minami, Nagoya 457, Japan
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.

Consider an end Ω in the sense of Heins (cf. Heins [3]): Ω is a relatively non-compact subregion of an open Riemann surface such that the relative boundary ∂Ω consists of finitely many analytic Jordan closed curves, there exist no non-constant bounded harmonic functions with vanishing boundary values on ∂Ω and Ω has a single ideal boundary component. A density P = P(z)dxdy (z = x + iy) is a 2-form on Ω∩∂Ω with nonnegative locally Holder continuous coefficient P(z).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 132 , December 1993 , pp. 131 - 139
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1993

References

[1] Ahlfors, L. and Sario, L., Riemann Surfaces, Princeton, 1960.Google Scholar
[2] Hayashi, K., Les solutions positives de l’équation Δu = Pu sur une surface de Riemann, Kōdai Math. Sem. Rep., 13 (1961), 20–24.Google Scholar
[3] Heins, M., Riemann surfaces of infinite genus, Ann. of Math., 55 (1952), 296–317.Google Scholar
[4] Kawamura, M., Picard principle for finite densities on Riemann surfaces, Nagoya Math. J., 67 (1977), 35–40.Google Scholar
[5] Kusunoki, Y., On Riemann’s period relations on open Riemann surfaces, Mem. Coll. Sci. Kyoto Univ. Ser. A Math., 30 (1956), 1–22.Google Scholar
[6] Miranda, C., Partial Differential Equations of Elliptic Type, Springer, 1970.Google Scholar
[7] Nakai, M., Picard principle and Riemann theorem, Tôhoku Math. J., 28 (1976), 277–292.Google Scholar
[8] Nakai, M., Picard principle for finite densities, Nagoya Math. J., 70 (1978), 7–24.Google Scholar
[9] Segawa, S., A duality relation for harmonic dimensions and its applications, Kodai Math., J., 4 (1981), 508–514.Google Scholar
[10] Shiga, H., On harmonic dimensions and bilinear relations on open Riemann surfaces, J. Math. Kyoto Univ., 21 (1981), 861–879.Google Scholar