Principal Investigator: Guofang Wei
This proposal is concerned with several problems centered around Ricci curvature. Recent development shows the extraordinary power of Ricci flow. It thus deserves studies from various viewpoints. The principal investigator will study Ricci flow and comparison geometry, stability of Ricci flow and compact Einstein manifolds. The principal investigator will also study obstructions for noncompact Einstein 4-manifolds and the Gromov-Hausdorff limits of manifolds with Ricci curvature lower bound.
Geometric objects such as manifolds appear naturally in science and engineering, as configuration spaces, as Einsten's model of universe. Ricci curvature is a fundamental concept in geometry as well as Einstein's general relativity. Einstein manifolds are important both in mathematics and physics. They are good candidates for canonical metrics on general Riemannian manifolds and they are the vacuum solutions of Einstein's field equation (with cosmological constant) in general relativity. General relativity is the study of gravity, the one fundamental force that should play a crucial role in understanding our universe. Thus the fundamental research in these areas should not only be important in its own right but also should have implications in science and engineering.
