Mathematical Sciences: Differential Geometry, Partial Differential Equations and Several Complex Variables

数学科学：微分几何、偏微分方程和多个复变量

• 批准号: 8801999
• 负责人: Robert Greene
• 金额: $ 31.41万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801999&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Differential; Geometry; Partial

Robert Greene and Shiu-Yuen Cheng will continue their work in the geometry and function theory of complex manifolds. The use of methods of metric geometry in complex analysis has a long history, much of the recent work involves the construction of invariant metrics. They will be joined by Gerard Walschap who will investigate certain interesting types of submanifolds of manifolds with nonnegative sectional curvature. Greene's research will concentrate on the following three areas: differential geometric several complex variables; Riemannian geometry of noncompact and compact manifolds; fixed points of smooth maps of manifolds. Cheng will investigate Liouville type theorems for harmonic functions and minimal hypersurfaces with finite total curvature. Walschap will consider the codimension two case of the so-called soul theorem. This involves the investigation of compact, totally convex and totally geodesic submanifolds.

罗伯特·格林和郑少元将继续他们在复流形的几何和函数理论方面的工作。度量几何方法在复杂分析中的应用有很长的历史，最近的许多工作都涉及不变度量的构造。Gerard Walschap将加入他们的行列，他将研究具有非负截面曲率的流形中某些有趣类型的子流形。Greene的研究将集中在以下三个领域：微分几何、几个复变量；非紧致和紧致流形的黎曼几何；流形上光滑映射的不动点。程将研究调和函数和有限全曲率极小超曲面的Liouvile型定理。Walschap将考虑所谓灵魂定理的余维2情形。这涉及到紧致的、完全凸的和完全测地子流形的研究。