Fundamental gaps of spherical triangles

Abstract

We show that the spherical equilateral triangle of diameter $\frac{\pi }{2}$ is a strict local minimizer of the fundamental gap on the space of the spherical triangles with diameter $\frac{\pi }{2}$, which partially extends Lu-Rowlett’s result–(Commun Math Phys 319(1): 111–145, 2013) from the plane to the sphere.