Mathematical Sciences: Existence of Many Minimal Surfaces onRiemannian Manifolds and Applications in Geometry and Topology

数学科学：黎曼流形上许多极小曲面的存在性及其在几何和拓扑学中的应用

• 批准号: 9307221
• 负责人: Jon Pitts
• 金额: $ 8.35万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9307221&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Existence; Many; Minimal

The research entails studies of analytic and topological properties of classes of minimal surfaces in Riemannian manifolds of dimension greater than or equal to 3. The methods are primarily those of geometric measure theory and are expected to achieve further insight to the analytic and topological structures of hypersurfaces lying in these manifolds. Particular attention will be paid to dimension 3 where new techniques are applied to show that certain Riemann surfaces can be realized as minimal types.

这项研究需要研究分析和拓扑 黎曼流形中极小曲面类的性质 尺寸大于或等于3。 所述方法 主要是几何测量理论，预计将 实现进一步的洞察力，分析和拓扑 这些流形中的超曲面的结构。 特别 注意力将集中在第三个维度， 应用表明，某些黎曼曲面可以实现为 最小类型。