Shoo Seto, California State University, Fullerton

Title: Fundamental gap on spheres

Abstract: Estimating the gap between the first two eigenvalues,
the fundamental gap, of the Laplacian or more generally the
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 the Euclidean space
in 2011 and conjectured similar results holds for spaces with constant
sectional curvature. In this talk we discuss the fundamental gap of
convex domains on spheres and in a recent work, we partially extend a
result of Z.Lu and J. Rowlett on the fundamental gap of triangles to
the case of spherical triangles. This is joint work (in various
subsets) with Xianzhe Dai, Lili Wang, Guofang Wei, and Xuwen Zhu.