Alexandrov Geometry and Applications

[摘要]获奖：DMS 1309340，首席研究员：Anton petrunin首席研究员建议继续研究Alexandrov几何及其应用，包括等长群作用和黎曼几何。研究主要分为以下几个部分：(1)寻找与欧几里得空间上等距作用有关的CAT[0]空间的新例子；(2)黎曼流形的坍缩与收敛；(3)纯Alexandrov几何。亚历山德罗夫几何从公理化的角度研究度量空间，这类似于欧几里得元素中给出的方法。这个理论在现代几何的许多分支中都有应用。除了纯粹的研究之外，首席研究员还建议与合著者一起继续他的工作，撰写一本旨在成为该几何领域全面文本和参考的书；他还有另外两个较小的几何教育项目。

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.