Mathematical Sciences: Pseudodifferential Techniques for Degenerate Elliptic Equations in Geometry

数学科学：几何中简并椭圆方程的伪微分技术

• 批准号: 9001702
• 负责人: Rafe Mazzeo
• 金额: $ 6.5万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001702&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Pseudodifferential; Techniques; Degenerate

The principal investigator will study pseudodifferential techniques in the study of degenerate elliptic equations with applications to geometry. He will extend techniques to determine a spectral analysis of the Hodge-Laplace operator acting on differential forms on complete asymptotic hyperbolic manifolds of infinite volume and on geometrically finite quotients of hyperbolic space. Related projects involve the study of the relationship between unique continuation theorems for the Laplacian at infinity and the presence of negative curvature. For many years mathematicians have studied the behavior of certain differential operators on hypersurfaces which extend off to infinity. This study has its origins in the calculus of Newton. In this project the principal investigator will analyze operators which have large variations over very large domains "near" infinity. In the past, only progress on operators which have small local variations was made.

首席研究者将研究拟南芥椭圆形方程的伪差技术，并应用于几何形状。 他将扩展技术以确定作用于无限量无限体积的差异形式的Hodge-Laplace操作员的光谱分析，以及在双曲空间的几何有限的商上。 相关项目涉及研究无穷大的Laplacian独特延续定理与存在负曲率之间的关系。 多年来，数学家一直在研究某些差异操作员在延伸至无限远的高度曲面上的行为。 这项研究起源于牛顿的微积分。 在该项目中，首席研究人员将分析运营商在“接近”无穷大的非常大的领域上有很大的变化。 过去，只有在局部变化较小的操作员上进行的进展。