Date of Award
8-17-2016
Document Type
Thesis
Abstract
We use the conformal method to investigate solutions of the vacuum Einstein constraint equations on a manifold with a Yamabe-positive metric. To do so, we develop a model problem with symmetric data on Sn⁻¹ x S¹. We specialize the model problem to a two-parameter family of conformal data, and find that no solutions exist when the transverse-traceless tensor is identically zero. When the transverse traceless tensor is nonzero, we observe an existence theorem in both the near-constant mean curvature and far-from-constant mean curvature regimes.
Recommended Citation
Knowles, Tyler D., "An existence theorem for solutions to a model problem with Yamabe-positive metric for conformal parameterizations of the Einstein constraint equations" (2016). Mathematics and Statistics . 8.
https://ualaska.researchcommons.org/uaf_grad_math_stats/8
Handle
http://hdl.handle.net/11122/6811