Type
Text
Type
Dissertation
Advisor
Khuri, Marcus A | Ebin, David G | Anderson, Michael T | Douglas, Michael R.
Date
2012-05-01
Keywords
Mathematics | Compacness, Manifolds with boundary, Yamabe problem
Department
Department of Mathematics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/71203
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
We study the problem of conformal deformation of Riemannian structure to constant scalar curvature with zero mean curvature on the boundary. We prove compactness for the full set of solutions when the boundary is umbilic and the dimension $n \leq 24$. The Weyl Vanishing Theorem is also established under these hypotheses, and we provide counter-examples to compactness when $n \geq 25$. Lastly, our methods point towards a vanishing theorem for the umbilicity tensor, which is anticipated to be fundamental for a study of the nonumbilic case. | 116 pages
Recommended Citation
Disconzi, Marcelo Mendes, "Compactness and Non-compactness for the Yamabe Problem on Manifolds With Boundary" (2012). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 409.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/409