Sharp inequalities for heat kernels of Schrodinger operators and applications to spectral gaps

This paper derives inequalities for multiple integrals from which sharp inequalities for ratios of heat kernels and integrals of heat kernels of certain Schrodinger operators follow. Such ratio inequalities imply sharp inequalities for spectral gaps. The multiple integral inequalities, although very different, are motivated by the now classical Brascamp-Lieb Luttinger rearrangement inequalities. (C) 2000 Academic Press.