CONFORMAL PERTURBATIONS AND LOCAL SMOOTHING

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  • March 20, 2019
Creator
  • Muckerman, Dylan
    • Affiliation: College of Arts and Sciences, Department of Mathematics
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.
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  • In Copyright
Advisor
  • Marzuola, Jeremy
  • Taylor, Michael
  • Metcalfe, Jason
  • Christianson, Hans
  • Williams, Mark
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2018
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