Asymptotic geometry, filling functions, and non-positive curvature

渐近几何、填充函数和非正曲率

• 批准号: 399394-2011
• 负责人: Young, Robert
• 金额: $ 1.17万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=529305
• 关键词: Asymptotic; geometry; filling; functions; non

I plan to study the large-scale geometry of groups and spaces. One way to study a space is to look at curves and discs. A space where every curve is the boundary of some disc is called simply connected. Even if you know that a space is simply connected, you may not know how big those discs are; in some spaces, there are short loops which can only be filled by very large discs. Problems like these, where one knows that something exists, but one wants to know how big it is, are problems in quantitative geometry.

我计划研究群体和空间的大尺度几何。 研究空间的一种方法是观察曲线和圆盘。 一个空间中的每一条曲线都是某个圆盘的边界，这个空间叫做单连通的。 即使你知道一个空间是单连通的，你也可能不知道这些圆盘有多大;在某些空间中，有一些短的环，只能由非常大的圆盘填充。 像这样的问题，人们知道某样东西存在，但想知道它有多大，是定量几何中的问题。