Mathematical Sciences: Foundations of Integral Geometry

数学科学：积分几何基础

• 批准号: 8902400
• 负责人: Joseph H. Fu
• 金额: $ 3.04万
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902400&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Foundations; Integral; Geometry

The principal investigator will find a natural class of objects on which curvature measures are well-defined and satisfy the kinematic formula. It is expected that such a class will consist of the zero-sets of non-negative "Monge-Ampere" functions satisfying certain additional assumptions. He will investigate whether curvature measures are intrinsic invariants. Alexandrov's theory of intrinsic curvature of surfaces to higher dimensions will be generalized. The geometry of non-smooth objects can be studied from a unified point of view when scalar-valued curvatures are thought of as measures. No comprehensive theory of curvature measures embraces both convex sets and singular algebraic varieties. The principal investigator will use his recently developed methods involving geometric measure theory to further clarify this problem. New tools using these techniques will be created.

首席研究员会发现一种天然的 曲率度量定义明确并满足以下条件的对象 运动学公式 预计这样的课程将 由非负的“Monge-Ampere”函数的零集组成 满足某些额外的假设。 他会调查的 曲率度量是否是固有不变量。 Alexandrov曲面的内曲率理论 维度将被推广。 非光滑物体的几何形状可以从 统一的观点时，标量值曲率被认为是 作为措施。 没有全面的曲率测度理论 包含凸集和奇异代数簇。 的 首席研究员将使用他最近开发的方法 涉及几何测度理论来进一步阐明这一点 问题. 将创建使用这些技术的新工具。