2016 Theses Doctoral

# Quasi-local energy and isometric embedding

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.

## Files

- Gimre_columbia_0054D_13351.pdf application/pdf 377 KB Download File

## More About This Work

- Academic Units
- Mathematics
- Thesis Advisors
- Wang, Mu-Tao
- Degree
- Ph.D., Columbia University
- Published Here
- May 4, 2016