活动地点：CMS 201

活动类型：学术报告

主讲人：韦国芳教授

活动时间：2016-07-25 09:30:00--2016-07-25 10:30:00

活动内容：

韦国芳教授专题学术报告

报告题目：Sharp Fundamental Gap Estimate on Convex Domains of Sphere

报告人：韦国芳 教授（加州大学圣巴巴拉分校数学系）

时间：2016年7月25日（周一）上午09:30

地点：数学中心201教室

Abstract: In their celebrated work, B. Andrews and J. Clutterbuck proved the fundamental gap (the difference between the first two eigenvalues) conjecture for convex domains in the Euclidean space and conjectured similar results holds for spaces with constant sectional curvature. We prove the conjecture for the sphere. Namely when $D$, the diameter of a convex domain in the unit $S^n$ sphere, is $\le \frac{\pi}{2}$, the gap is greater than the gap of the corresponding $1$-dim sphere model. We also prove the gap is $\ge 3\frac{\pi^2}{D^2}$ when $n \ge 3$, giving a sharp bound.  As in B. Andrews and J. Clutterbuck's work, the key is to prove a super log-concavity of the first eigenfunction. This is a joint work with S. Seto and L. Wang.