Mathematical Sciences: Stability Problems In The Theory Of Convex Sets

数学科学：凸集理论中的稳定性问题

• 批准号: 8701893
• 负责人: Helmut Groemer
• 金额: $ 8.3万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-01 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701893&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Stability; Problems; Theory

Helmut Groemer will carry out research into stability problems associated with convex sets. Many theorems in the theory of convex sets state that under certain conditions a body is of an important special type or that two bodies are related to one another in a particular way. Corresponding to such results it is often easy to pose an associated stability problem. For example one might ask how close a body is to being a ball in terms of its isoperimetric deficit. The investigator has already made some progress in this direction notably in the case of results connected with projections of convex bodies. His future research will focus on stability problems associated with the Brunn-Minkowski theorem, symmetrization procedures, inscribed and circumscribed bodies. The anticipated techniques will involve geometric adaptations of spherical harmonics and Radon transforms.

Helmut Groemer将进行稳定性研究 与凸集相关的问题。理论中的许多定理 凸集理论指出，在一定条件下，物体是 一个重要的特殊类型，或者两个物体与一个物体有关 另一个以某种方式。对应于这样的结果， 通常容易引起相关的稳定性问题。例如 有人可能会问，从物体的形状来看， 等周差 调查人员已经在这方面取得了一些进展 特别是在结果与以下方面有关的情况下， 凸体的投影。他未来的研究将集中在 与Brunn-Minkowski定理相关的稳定性问题， 对称化程序，内接和外接机构。 预期的技术将涉及几何调整， 球谐函数和Radon变换。