Differential Geometry Seminar: Fundamental Gap Estimate for Integral Ricci Curvature

Seminar | September 23 | 3-4 p.m. | 939 Evans Hall

 Guofang Wei, UC Santa Barbara

 Department of Mathematics

The fundamental gap is the difference of the first two eigenvalues of the Laplacian. We will first review some recent work on the fundamental gap estimates for convex domains on Euclidean spaces and sphere. Then we present several fundamental gap estimates in terms of integral Ricci curvature, including a sharp Zhong-Yang type eigenvalue lower bound for closed Riemannian manifolds with control on integral Ricci curvature. This part is a joint work with X. Ramos, S. Seto, and Q. S. Zhang.