91涩漫

Title:听The fundamental gap in hyperbolic space.

Abstract:听The fundamental gap is the difference between the first two eigenvalues of the Dirichlet problem of the Laplace operator with convex potential. We give a brief overview of the results in Euclidean space then talk about the unexpected behavior of the fundamental gap in hyperbolic space. We present two types of questions related to the fundamental gap: the first type, which deals with bounding the gap from below has received a lot of attention; the second type is about the optimality of the constant potential. We found recently that the constant potential is not the one that provides the best lower bound.

听