Vol. 23, No. 3, 1967

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Vol. 285: 1  2
Vol. 284: 1  2
Vol. 283: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
An extremal length criterion for the parabolicity of Riemannian spaces

Wellington Ham Ow

Vol. 23 (1967), No. 3, 585–590
Abstract

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
Milestones
Received: 30 January 1967
Published: 1 December 1967
Authors
Wellington Ham Ow