CONFORMAL PERTURBATIONS AND LOCAL SMOOTHING Public Deposited
- Last Modified
- 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.
- Date of publication
- August 2018
- Keyword
- DOI
- Resource type
- Rights statement
- 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
- Language
- Parents:
This work has no parents.
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Muckerman_unc_0153D_18101.pdf | 2019-04-07 | Public |
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