Radial quasiharmonic functions

Leo Sario and Cecilia Wang

Vol. 46 (1973), No. 2, 515–522

DOI: 10.2140/pjm.1973.46.515

Abstract

A function s on a Riemannian manifold is called quasi-harmonic if it satisfies Δs = 1, where Δ is the Laplace-Beltrami operator dδ + δd. Existence of quasiharmonic functions with various boundedness properties has thus far been investigated by means of useful implicit tests. We now ask: Can such functions be formed by direct construction, in a manner accessible to computation if need be?

Mathematical Subject Classification 2000

Primary: 31B99

Milestones

Received: 18 April 1972

Revised: 15 November 1972

Published: 1 June 1973