Asymptotic Expansions of Solutions of the Yamabe Equation near Isolated Singular Points

Doctoral Dissertation

Abstract

We study asymptotic behaviors of positive solutions to the Yamabe equation near isolated singularities and establish expansions up to arbitrary orders. Such results generalize an earlier pioneering work by Caffarelli, Gidas, and Spruck, and a work by Korevaar, Mazzeo, Pacard, and Schoen. Then, we study the existence of solutions with prescribed asymptotic expansions near singular points and an arbitrarily high order of approximation.

Attributes

Attribute NameValues
Author Yichao Li
Contributor Matthew Gursky, Committee Member
Contributor Qing Han, Research Director
Contributor Mei-Chi Shaw, Committee Member
Contributor Alex Himonas Alexandrou, Committee Member
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name Doctor of Philosophy
Banner Code
  • PHD-MATH

Defense Date
  • 2020-03-27

Submission Date 2020-04-06
Record Visibility Public
Content License
  • All rights reserved

Departments and Units
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