Mathematical Sciences: Symplectic Manifolds, Minimal Surfaces and Mapping Class Groups

数学科学：辛流形、最小曲面和映射类群

• 批准号: 9305067
• 负责人: Jon Wolfson
• 金额: $ 3.5万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-15 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9305067&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Symplectic; Manifolds; Minimal

Wolfson The research entails the study of minimal surfaces in Kaehler- Einstein manifolds. Of particular interest are those of the stable kind where the second variation of the energy of the map is positive definite. It intended to show that there exist stable minimal surfaces in Ricci-flat K3 surafces which are non- holomorphic for any compatible complex structure. This research may have applications to other areas of mathematics such as algebraic geometry as well as to some branches of modern mathematical physics.

沃尔夫森这项研究需要研究Kaehler-Einstein流形中的极小曲面。特别令人感兴趣的是那些稳定的类型，其中映射的能量的第二个变化是正定的。证明了在Ricci-Flat K3曲面中存在稳定的极小曲面，它们对于任意相容的复结构都是非全纯的。这项研究可能会应用到其他数学领域，如代数几何以及现代数学物理的一些分支。