Simply connected nonpositively curved surfaces in ℝ³

Hsungrow Chan

Vol. 223 (2006), No. 1, 1–4

DOI: 10.2140/pjm.2006.223.1

Abstract

We consider complete noncompact simply connected nonpositively curved surfaces that are twice continuously differentiably embedded in Euclidean three space. If such a surface has square integrable second fundamental form, then it must be a plane.

Keywords

simply connected, nonpositively curved surfaces, minimal surfaces

Mathematical Subject Classification 2000

Primary: 53A05, 49Q05

Milestones

Received: 7 March 2004

Revised: 24 December 2004

Accepted: 11 May 2005

Published: 1 January 2006