About small eigenvalues of the Witten Laplacian

Abstract

We study the low-lying eigenvalues of the semiclassical Witten Laplacian associated to a Morse function $\phi$. Compared to previous works we allow general distributions of critical values of $\phi$, for instance allowing all the local minima to be absolute. The motivation comes from metastable dynamics described by the Kramers–Smoluchowski equation.