Mathematical Sciences: Applications of Variational Problems on Riemann Surfaces to Low-Dimensional Geometry

数学科学：黎曼曲面变分问题在低维几何中的应用

• 批准号: 9300001
• 负责人: Michael Wolf
• 金额: $ 6万
• 依托单位: William Marsh Rice University
• 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: 1993-06-01 至 1997-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9300001&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Applications; Variational; Problems

The Principal Investigator proposes to study some variational problems on Riemann Surfaces that have applications to the study of the Moduli space of curves and three dimensional hyperbolic geometry. Specifically, he proposes to study an extremal length problem on a Riemann surface the solution of which would lead to new invariants of Riemann surfaces, and then new local functions on Moduli space. He also proposes to study the shapes of images of harmonic maps of surfaces in hyperbolic three-manifolds, including the differential-topological singularities of the images, and the dependence of the motion of the image surface in the three-manifold upon the motion of the domain in Teichmuller space.

主要研究者提出研究黎曼曲面上的一些变分问题，这些变分问题可应用于曲线的模空间和三维双曲几何的研究。 具体而言，他建议研究一个极值长度问题的黎曼曲面的解决方案，将导致新的不变量的黎曼曲面，然后新的地方职能的模空间。 他还建议研究形状的图像调和映射的表面在双曲三流形，包括微分拓扑奇点的图像，并依赖于运动的图像表面在三流形上的运动域在Teichmuller空间。