In this thesis, we consider the recent definition of gravitational energy at the quasi-local level provided by Mu-Tao Wang and Shing-Tung Yau. Their definition poses a variational question predicated on isometric embedding of Riemannian surfaces into the Minkowski space; as such, there is a naturally associated Euler-Lagrange equation, which is a fourth-order system of partial differential equations for the embedding functions. We prove a perturbation result for solutions of this Euler-Lagrange equation.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/D8765FB1 |
| Date | January 2016 |
| Creators | Gimre, Karsten Trevor |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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