Collections > Electronic Theses and Dissertations > CONFORMAL PERTURBATIONS AND LOCAL SMOOTHING

The purpose of this paper is to study the effect of conformal perturbations on the local smoothing effect for the Schrödinger equation on surfaces of revolution. The paper [CW13] studied the Schrödinger equation on surfaces of revolution with one trapped orbit. The dynamics near this trapping were unstable, but degenerately so. Beginning from the metric g from these papers, we consider the perturbed metric g_s = e^sf g, where f is a smooth, compactly supported function. If s is small enough and finitely many derivatives of f satisfy an appropriate bound, then we show that a local smoothing estimate still holds.