Year: 2020
Type: article
Abstract: We prove that every properly embedded minimal annulus in $\mathbb{S}^2\times\mathbb{R}$ is foliated by circles. We show that such minimal annuli are given by periodic harmonic maps $\mathbb{C} \to \mathbb{S}^2$ 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.
Source: Journal of Integrable Systems
Authors: L Hauswirth, M Kilian, M U Schmidt
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W1503495368