Learn More
We give a lower bound for the first gap λ2 − λ1 of the Dirichlet eigenvalues of the Schrödinger operator on a bounded convex domain Ω in a class of Riemannian manifolds, namely λ2 − λ1 ≥ π diameter(Ω) + ( 12 π − 1)α. For the Laplacian on disks in Rn, we have λ2 − λ1 ≥ 4 3 π diameter(Ω) .