PDE Seminar Abstracts

Lower bounds for the fundamental gap

Julie Clutterbuck
Australian National University
29 Mar 2010 3-4pm, Carslaw Room 273


We consider the eigenvalues of a Schrödinger operator with convex potential on a convex domain. The Gap Conjecture states that the difference between the first two eigenvalues has a lower bound approached by a long, thin, rectangular domain with constant potential. In joint work with Ben Andrews, we prove this conjecture. Our method also characterises the gap for non-convex potentials.