Title：Fundamental gap of convex domains in the sphere

Speaker：Chenxu He (University of California, Riverside)

Time：2017年7月7日（星期五)）   下午2:30--3:30

Room：东区管理科研楼  数学科学学院1518室

Abstract：For a bounded convex domain on aRiemannian manifold, the fundamental gap is the difference of the first twonon-trivial Dirichlet eigenvalues. In their celebrated work, B. Andrews and J.Clutterbuck proved the fundamental gap conjecture for convex domains in theEuclidean space, showing that the gap is at least as large as the one for aone-dimensional model. They also conjectured that similar results hold forspaces with constant sectional curvature. Very recently, on the unit sphere,Seto-Wang-Wei proved that the fundamental gap is greater than the gap of theone dimensional sphere model, in particular, ≥ 3 π^2/D^2 (n ≥ 3), provided the diameter of the domainD ≤ π/2. In a joint work with Guofang Wei atUCSB, we extend Seto-Wang-Wei’slower bound estimate to all convex domains in the hemisphere.