Constrained Willmore surfaces

约束 Willmore 曲面

• 批准号: 15028839
• 负责人: Professor Dr. Franz Pedit
• 金额: --
• 依托单位: Department of Mathematics and Statistics
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2005
• 资助国家: 德国
• 起止时间: 2004-12-31 至 2010-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/15028839?language=en
• 关键词: Constrained; Willmore; surfaces

The Willmore functional or elastic bending energy W — ∫ H2 of an immersion is a global invariant of fundamental importance in contemporary surface theory and applications ranging from the biophysics of membranes to string theory. We investigate the so-called constrained Willmore surfaces which are conformal immersions of a Riemann surface that are critical points of VV under compactly supported infinitesimal conformal variations. During the third period of the project the focus of our investigations is on finding estimates for the Willmore energy of constrained Willmore tori. These can all be constructed by methods of complex algebraic geometry which suggests that the fundamental algebraic geometric invariants like the degree of certain appendant holomorphic maps or the genus of the so called spectral curve should be related to the Willmore energy of the immersion. For several special cases we can establish such a link and our plan is to generalize the obtained estimates to arbitrary constrained Willmore tori.

Willmore函数或弹性弯曲能W -λ H2的浸没是一个全球不变的基本重要性，在当代表面理论和应用范围从生物物理学的膜弦理论。我们研究了所谓的约束Willmore表面，这是共形浸入的黎曼曲面，是临界点的VV下紧支持的无穷小共形变化。在第三阶段的项目中，我们的调查重点是寻找估计的Willmore能源约束Willmore环面。这些都可以通过复代数几何的方法来构造，这表明基本的代数几何不变量，如某些附加全纯映射的度数或所谓谱曲线的属，应该与浸没的Willmore能量有关。对于几种特殊情况，我们可以建立这样的链接，我们的计划是推广所获得的估计任意约束Willmore环面。