Axial minimal surfaces in $S^2 x R$ are helicoidal
Axial minimal surfaces in $S^2 x R$ are helicoidal
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.