Axial minimal surfaces in S^2 x R are helicoidal

Abstract

We prove that if a complete, properly embedded, finite-topology minimal surface in S^2 x R contains a line, then its ends are asymptotic to helicoids, and that if the surface is an annulus, it must be a helicoid.

7 pages. The revised version corrects a minor error on page 5

References in corpus (2)

• On the number of minimal surfaces with a given boundary
• Conformal Structure of Minimal Surfaces with Finite Topology