Eigenvalue problems for the Schrödinger operator with the magnetic field on a compact Riemann manifold (Q1093966)

Let M be a compact Riemannian manifold and H the Schrödinger operator with magnetic field defined on M. In the paper under review using the Malliavin calculus and the technique of Wiener functionals the author gives a representation of the least eigenvalue of H by the variational formula and proves that it is closely related with the asymptotic behaviour of the semigroup \(\{e^{-tH}\}_{t\geq 0}\) as \(t\to \infty\).