Vol. 23, No. 3, 1967

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
An extremal length criterion for the parabolicity of Riemannian spaces

Wellington Ham Ow

Vol. 23 (1967), No. 3, 585–590

It is the purpose of this paper to show that a given Riemannian space satisfying a regularity condition is parabolic if and only if the extremal distance of a fixed ball in the space from the ideal boundary of the space is infinite. We will also show that the harmonic modulus of a space bounded by two sets of boundary components coincides with the extremal distance between the two sets.

Mathematical Subject Classification
Primary: 53.72
Received: 30 January 1967
Published: 1 December 1967
Wellington Ham Ow