Minimizer of the Willmore energy with prescribed rectangular conformal class

具有规定的矩形共形类的威尔莫尔能量的最小化

• 批准号: 339809664
• 负责人: Professorin Dr. Lynn Heller
• 金额: --
• 依托单位: Fachbereich Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/339809664?language=en
• 关键词: Minimizer; Willmore; energy; prescribed; rectangular

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.

在这个项目中，我们的目标是确定所有环面在3-空间最小化的Willmore功能与规定的矩形共形型相结合的方法，从可积系统理论和整体分析。候选人给出的真实的分析家庭的约束Willmore环面开始在Clifford环面以下的均匀环面，分叉在第一个分叉点的2-lobed Delaunay环面和收敛到双覆盖球的共形型退化。将猜想推广到矩形共形类的开邻域。特别是，适当的候选人在这些共形类将被构造，到目前为止，只有那些在一个小的邻域的克利福德环面是已知的。