The classification of minimal annuli in S2xR and CMC tori in S3 via integrable system
Prof. Dr. Laurent Hauswirth (Université de Marne la Vallée)
08 November 2016, 15:45 - 16:45, HG G 43
10 November 2016, 13:15 - 15:00, HG G 43
17 November 2016, 13:15 - 15:00, HG G 43
Abstract
N. Hitchin introduced in 87 an algebraic correspondence between doubly-periodic harmonic map in S2 or S3 (the three dimensional sphere) with hyperelliptic Riemann surfaces S, called spectral curves. The period problem depends on the existence of an Abelian differential dh with prescribed poles on S. I will describe the construction of (S, dh) related to CMC annuli immersed in S3 and minimal annuli in S2xR. We will study the differential structure on the space moduli of these surfaces induced by this representation. We describe how to navigate in the space of Alexandrov embedded surfaces by deformation of (S, dh). A global study of this algebraic representation give a complete classification of embedded CMC tori in S3 via integrable system. Similar considerations will characterize a two-parameter family of annuli foliated by constant curvature curves in S2xR as the unique properly embedded minimal annuli.