BZ Seminar in Analysis: Rick Schoen (University of California, Irvine)

An extension problem for Riemannian metrics

The problem of extending a given metric on a finite three dimensional domain to one which is asymptotically flat and which satisfies the constraint equations of general relativity was proposed by Robert Bartnik. He proposed that the minimal mass of such an extension would be a measure of the quasi-local mass of the domain and this is called the Bartnik mass. In this talk we will describe this problem and recent results on it including a comparison of the Bartnik mass to other quasi-local mass notions. 

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