Colloquium

Alina Stancu, Concordia University

"On the fundamental gap of convex domains in hyperbolic space"

The difference between the first two eigenvalues of the Dirichlet Laplacian on convex domains of R^n and, respectively S^n, satisfies the same strictly positive lower bound depending on the diameter of the domain. In work with collaborators, we have found that the gap of the hyperbolic space on convex sets behaves strikingly different even if a stronger notion of convexity is employed. This is very interesting as many other features of first two eigenvalues behave in the same way on all three spaces of constant sectional curvature. 

MC 5501