Seminario de geometría diferencial y sistemas dinámicos, CIMAT

Fecha y lugar: Lunes 14 sept 2020, 4:00, en linea (BlueJeans)

Speaker: Shoo Seto, California State University, Fullerton, USA

Title: Fundamental gap on spheres

Abstract: Estimating the gap between the first two eigenvalues of the Laplacian, the "fundamental gap", or more generally, of Schrodinger operators, is important both in mathematics and physics. In their celebrated work, B. Andrew and J. Clutterbuck proved the fundamental gap conjecture for convex domains in Euclidean space in 2011 and conjectured that similar results hold for spaces with constant sectional curvature. In this talk we discuss the fundamental gap of convex domains on spheres. In a recent work, we partially extended a result of Z. Lu and J. Rowlett on the fundamental gap of plane triangles to the case of spherical triangles. This is joint work (in various subsets) with Xianzhe Dai, Lili Wang, Guofang Wei, and Xuwen Zhu.