Constrained Willmore surfaces

约束 Willmore 曲面

• 批准号: 5406556
• 负责人: Professor Dr. Alexander I. Bobenko
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2003
• 资助国家: 德国
• 起止时间: 2002-12-31 至 2007-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5406556?language=en
• 关键词: Constrained; Willmore; surfaces

We want to study a class of surfaces in 3-space, the so-called "constrained Willmore surfaces". These are defined as the critical points of the Willmore function when only those variations are allowed that preserve the conformal type of the surface. This class of surfaces is invariant under Möbius transformations of the ambient space. Examples include constant mean curvature surfaces in Euclidean space, hyperbolic space and the 3-sphere. Our main interest is the construction and classification of new compact examples, mainly topological spheres and tori. We hope to obtain explicit formulas for all constrained Willmore spheres and tori from a soliton theoretic approach.

我们想要研究三维空间中的一类曲面，即所谓的“约束Willmore曲面”。当只允许保持曲面保形类型的变化时，这些点被定义为Willmore函数的临界点。这类曲面在环境空间的Möbius变换下是不变的。例如，欧几里德空间、双曲空间和三球面上的常平均曲率曲面。我们的主要兴趣是新紧致例子的构造和分类，主要是拓扑球和环面。我们希望从孤子理论的角度得到所有受约束的Willmore球和环面的显式公式。