Mathematical Sciences: Differential Geometry

数学科学：微分几何

• 批准号: 8701404
• 负责人: Jon Wolfson
• 金额: $ 3.61万
• 依托单位: Tulane University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1989-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701404&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Differential; Geometry

The Principal Investigator will study a number of questions concerning maps of surfaces into a compact manifold. The maps under consideration will satisfy an elliptic partial differential equation. In particular he plans to study the structure of the moduli space of harmonic maps of the two-sphere into a homogeneous Kaehler manifold. He will also investigate minimal surfaces in the complex projective plane and study pseudo holomorphic curves with a view to applications in symplectic and other geometries. Jon Wolfson has established himself as one of the world leaders in the theory of harmonic maps. He has accumulated a vast repertory of techniques, such as the structure of semi-simple Lie groups, complex algebraic geometry and partial differential equations. The subject of harmonic maps has recently acquired prominence following the discovery of interesting global structure theorems on their moduli spaces. In addition the connections with minimal surface theory in low dimensional topology and with sigma-models in mathematical physics have led to a spectacular growth in the number of researchers in this area.

首席研究员将研究一些问题 关于曲面到紧致流形的映射。地图 在考虑将满足椭圆偏微分 方程特别是，他计划研究 二球面到A的调和映射的模空间 齐次Kaehler流形他还将调查最小的 复射影平面上的曲面，并研究伪 全纯曲线及其在辛和 其他几何形状。 乔恩·沃尔夫森已经成为世界上 调和映射理论的领导者他积累了大量的 技巧的储备，如半单李的结构 群、复代数几何和偏微分 方程 调和映射的主题最近获得了 在发现有趣的全球性 模空间上的结构定理此外 与低维极小曲面理论的联系 拓扑学和数学物理中的西格玛模型 这一领域的研究人员数量急剧增长， 区