The PI (principal investigator) plans to continue his researchprogram in metric and comparison geometry. The PI is pursuing to solve ormake progress on some basic problems in the following two areas: collapsedRiemannian manifolds with curvature bounded from below and positivelycurved manifolds with symmetry. In this research, mathematics from severaldisciplines interact, such as metric comparison geometry includingAlexandrov geometry, geometric analysis and topology. This project is buiton the early success by PI in the study of the collapsed Riemannianmanifolds with curvature bounded from above and below.Mathematics is the foundation of the natural sciences, anddifferential geometry and Riemannian geometry are among the most importantbranches that interact with other natural sciences such as physics. The PIis 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.
|Effective start/end date||6/15/08 → 5/31/11|
- National Science Foundation (National Science Foundation (NSF))