We prove that every properly embedded minimal annulus in |$mathbb{S}^2imesmathbb{R}$| is foliated by circles. We show that such minimal annuli are given by periodic harmonic maps |$mathbb{C} o mathbb{S}^2$| of finite type. Such harmonic maps are parameterized by spectral data, and we show that continuous deformations of the spectral data preserve the embeddedness of the corresponding annuli. A curvature estimate of Meeks and Rosenberg is used to show that each connected component of spectral data of embedded minimal annuli contains a maximum of the flux of the third coordinate. A classification of these maxima allows us to identify the spectral data of properly embedded minimal annuli with the spectral data of minimal annuli foliated by circles.
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