Minimizer of the Willmore energy with prescribed rectangular conformal class

在这个项目中，我们结合可积系统理论和整体分析的方法来确定三维空间中的所有环面，最小化具有规定的矩形保形类型的Willmore泛函。候选者由约束Willmore环面的实解析族给出，该解析族从齐次环面之后的Clifford环面开始，在第一个分岔点处分支到二瓣Delaunay环面，随着共形类型的退化收敛到双重覆盖球面。我们将研究将猜想推广到矩形共形类的开邻域。具体地说，这些保形类中的合适候选者将被构造出来，因为到目前为止，只有那些在克利福德环面附近的人是已知的。

In this project we aim at determining all tori in 3-space minimizing the Willmore functional with prescribed rectangular conformal type by combining methods from Integrable Systems Theory and Global Analysis. Candidates are given by the real analytic family of constrained Willmore tori starting at the Clifford torus following the homogenous tori, bifurcating at the first bifurcation point to the 2-lobed Delaunay tori and converging to the doubly covered sphere as the conformal type degenerates. Generalization of the conjecture to an open neighborhood of the rectangular conformal class will be investigated. In particular, appropriate candidates in these conformal classes will be constructed, as of now only those in a small neighborhood of the Clifford torus are known.