Some Problems in Riemannian Geometry

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

The PI (principal investigator) plans to continue his research program in metric and comparison geometry. The PI is pursuing to solve or make progress on some basic problems in the following two areas: collapsed Riemannian manifolds with curvature bounded from below and positively curved manifolds with symmetry. In this research, mathematics from several disciplines interact, such as metric comparison geometry including Alexandrov geometry, geometric analysis and topology. This project is buit on the early success by PI in the study of the collapsed Riemannian manifolds with curvature bounded from above and below. Mathematics is the foundation of the natural sciences, and differential geometry and Riemannian geometry are among the most important branches that interact with other natural sciences such as physics. The PI is pursuing to solve some basic problems in the above fields, which will have a broad intellectual impact. The PI will continue to actively pursue collaborations with other mathematicians in the United States and abroad, and speak at several national and international conferences in the next three years.