University of Connecticut

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Analysis Learning Seminar
Bartnik Boundary Conditions in General Relativity III
Zhongshan An (UConn)

Friday, December 6, 2019
3:30pm – 4:30pm

Storrs Campus
Monteith 214

The Bartnik boundary conditions are very well-known in general relativity. They play a key role when measuring the quasi-local mass of a bounded manifold with boundary. When the spacetime is static, Bartnik boundary conditions consists of the induced metric g and the mean curvature H on the boundary of the manifold. This pair (g,H) of boundary data is much studied by mathematicians, as they are closely related to not only Bartnik mass, but also various notions of quasi-local mass such as the Brown-York mass and the Hawking mass.

In general relativity, the existence of extensions of Bartnik boundary data which are Einstein manifolds is a very interesting and open problem. A fundamental question to approach this problem is whether the Bartnik boundary conditions are elliptic for the static/stationary vacuum spacetime.

In this mini course, I will start with an introduction to the ADM mass and the quasi-local mass in the first lecture. The second lecture will be devoted to discussions of Bartnik boundary data in the static spacetime, including the ellipticity and a local existence result. In the last lecture we will generalize these results from static to stationary spacetime.

Contact:

Matthew Badger (matthew.badger@uconn.edu)

Analysis Learning Seminar (primary), UConn Master Calendar

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