The first eigenvalue of analytic level surfaces on spheres
Sagun Chanillo · Mathematical Research Letters · 1994
A b s t r a c t .In this paper we establish a lower bound for the first eigenvalue of the Laplace-Beltrami operator of the level set of a real valued real-analytic function defined on spheres.The question of existence of such a lower bound was posed by P.Cordaro and J.Hounie and arose in their work on local solvability of systems of vector fields [CH].