Alexandrov's Geometry and Applications

PI proposes to continue his study of Alexandrov spaces and convergence and collapsing of Riemannian manifolds with lower curvature bounds.

Alexandrov geometry is a powerful technique in modern geometry.

It makes it possible to attack important conjectures via axiomatic methods similar to those of classical Euclidean geometry. At the same time it gives a more satisfactory form for many geometric results.