David Hoffman, Brian White
Abstract
We prove that if a complete, properly embedded, finite-topology minimal surface in $\mathbf{S}^2 \times \mathbf{R}$ contains a line, then its ends are asymptotic to helicoids, and that if the surface is an annulus, it must be a helicoid.
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We prove that if a complete, properly embedded, finite-topology minimal surface in $\mathbf{S}^2 \times \mathbf{R}$ contains a line, then its ends are asymptotic to helicoids, and that if the surface is an annulus, it must be a helicoid.
Key concepts: Helicoid, Minimal surface, Mathematics, Annulus (botany), Surface (topology), Geometry, Line (geometry), Topology (electrical circuits)