Alexandrov Geometry and Applications

Abstract

Award: DMS 1309340, Principal Investigator: Anton Petrunin

The 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.