University of North Carolina at Chapel Hill Graduate School
Doi
Abstract
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.Doctor of Philosoph
