Alexandrov Geometry and Applications

摘要奖：DMS 1309340，主要研究人员：Anton Petrunin主要研究人员建议继续研究亚历山大几何及其应用，包括等距群作用和黎曼几何。研究分为以下几个主要部分：(1)寻找与欧氏空间上的等距作用有关的CAT[0]空间的新例子；(2)黎曼流形的折叠和收敛；(3)纯Alexandrov几何。Alexandrov几何从公理的角度研究度量空间，这类似于欧几里德元素中给出的方法。这一理论在现代几何的许多分支中都有应用。除了纯粹的研究，首席研究人员建议继续与合著者合作写一本书，这本书旨在成为这一几何领域的全面文本和参考；他还有另外两个面向几何教育的较小项目。

AbstractAward: DMS 1309340, Principal Investigator: Anton PetruninThe principal investigator proposes to continue the study of Alexandrov geometry and its applications, which include isometric group actions and Riemannian geometry. The research is divided into the following main parts: (1) Finding new examples of CAT[0] spaces, related to isometric actions on Euclidean space, (2) Collapsing and convergence of Riemannian manifolds, and (3) Pure Alexandrov geometry.Alexandrov geometry studies metric spaces from an axiomatic point of view, which is similar to the approach given in Euclid's Elements. This theory has applications in many branches of modern geometry. In addition to to the pure research, the principal investigator proposes to continue his work with co-authors on a book which is intended to be a comprehensive text and reference in this area of geometry; he also has two other smaller projects oriented to geometric education.