Isoperimetric Inequalities

等周不等式

• 批准号: 0405707
• 负责人: Erwin Lutwak
• 金额: --
• 依托单位: Polytechnic University of New York
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0405707&HistoricalAwards=false
• 关键词: Isoperimetric; Inequalities

AbstractAward: DMS-0405707Principal Investigator: Erwin Lutwak, Deane Yang, Gaoyong ZhangThis project continues a long term program to develop extensionsand duals of the Brunn-Minkowski theory, which lies at the verycore of convex geometric analysis. This includes ongoinginvestigations of the partial differential equations that arisein these extensions. Generalizations of affine functionalsassociated with convex bodies are another central focus of theproposed work. A large part of the project concerns establishingsharp affine isoperimetric isoperimetric inequalities and relatedanalytic inequalities. The investigators will also continue theirefforts to understand better the connections between affineconvex geometric analysis and information theory.This project has potential for broader impact in many areas ofscience and engineering, because it deals with when and how canone reconstruct or approximate a geometric object from a limitednumber of geometric measurements. This is the central questionin many practical endeavors ranging from computer vision tomedical imaging. Some of the questions being studied by theinvestigators are sufficiently concrete that they can beexplained to and investigated by graduate, undergraduate, andeven high school students.

Abstractaward：DMS-0405707原理研究者：Erwin Lutwak，Deane Yang，Gaoyong Zhangthis项目继续进行了一个长期计划，以开发Brunn-Minkowski理论的扩展和双重，这是在Convex deemote分析的非常核心。 这包括对这些扩展的偏微分方程的持续进行评估。与凸体相关的仿射功能的概括是该工作的另一个核心重点。 该项目的很大一部分涉及建筑物的仿射等值等级不平等和相关的分析不平等。研究人员还将继续他们的工作人员，以更好地理解AffineConvex几何分析与信息理论之间的联系。该项目的潜力可能在许多科学和工程领域对许多领域产生更大的影响，因为它涉及何时以及如何从有限的几何测量值重建或近似几何对象。 这是许多实用的努力，包括计算机视觉Tomedical Imaging。评估者正在研究的一些问题足够具体，可以通过研究生，本科，十五个高中生来解释和调查。