Morse Index Bounds and Degeneration of Surfaces and Manifolds

莫尔斯索引界以及曲面和流形的退化

• 批准号: 0104453
• 负责人: Tobias Colding
• 金额: $ 25.55万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0104453&HistoricalAwards=false
• 关键词: Morse; Index; Bounds; Degeneration; Surfaces

Abstract for DMS - 0104453The goal of this project is to describe all embedded minimal surfaces of some fixed (but arbitrary) genus in a fixed (but arbitrary) closed 3-manifold. Such a study would include the description of these surfaces on a fixed small scale. Various applications of such a description will also be studied. In particular to the spherical space-form problem, the topology of 3-manifolds with positive scalar curvature and various other problems in the topology of 3-manifolds. Two other seperate projects will be investigated. One is simple closed geodesics on surfaces and another is degeneration of Kahler-Einstein manifolds.Roughly speaking the goal of this proposal is to describe all smooth soap-films. I soap-film is a surface spanning a boundary and which is critical for area among all other surfaces with the same boundary. Besides being a classical problem such a description would have many possible applications in a wide varieties of fields. Spanning from topology to mathematical biology.

DMS的摘要-0104453该项目的目的是描述在固定（但任意）封闭的3个manifold中某些固定（但任意）属的嵌入式最小表面。 这样的研究将包括对这些表面的描述。 此类描述的各种应用也将研究。 特别是在球形空间形式问题上，具有正标曲率的3个manifolds的拓扑结构和3个manifolds拓扑中的其他各种问题。 将调查另外两个分开的项目。 一种是表面上简单的封闭地球学，另一个是卡勒·因斯坦歧管的变性。该提案的目的是描述所有光滑的肥皂膜。 我的肥皂膜是跨越边界的表面，对于具有相同边界的所有其他表面之间的区域至关重要。 除了是一个经典问题之外，此类描述还将在各种各样的领域中具有许多可能的应用。 从拓扑到数学生物学跨越。