Removable singularities for subharmonic functions

Stephen J. Gardiner

Vol. 147 (1991), No. 1, 71–80

DOI: 10.2140/pjm.1991.147.71

Abstract

Let Ω be an open set in ℝⁿ (n ≥ 3) and S be a C²(n− 1)-dimensional manifold in Ω. Let α ∈ (0,n− 2) and E be a compact subset of S of zero α-dimensional Hausdorff measure. We show that, if s is subharmonic in Ω∖E and satisfies s(X) ≤ c[dist(X,S)]^α+2−n for X ∈ Ω∖S, then s has a subharmonic extension to the whole of Ω. The sharpness of this and other similar results is also established.

Mathematical Subject Classification 2000

Primary: 31B05

Milestones

Received: 15 February 1989

Published: 1 January 1991