Seminar series
Date
Mon, 28 Oct 2013
Time
17:00 -
18:00
Location
L6
Speaker
James Grant
Organisation
University of Surrey
We show that the positive mass theorem holds for
asymptotically flat, $n$-dimensional Riemannian manifolds with a metric
that is continuous, lies in the Sobolev space $W^{2, n/2}_{loc}$, and
has non-negative scalar curvature in the distributional sense. Our
approach requires an analysis of smooth approximations to the metric,
and a careful control of elliptic estimates for a related conformal
transformation problem. If the metric lies in $W^{2, p}_{loc}$ for
$p>n/2$, then we show that our metrics may be approximated locally
uniformly by smooth metrics with non-negative scalar curvature.
This talk is based on joint work with N. Tassotti and conversations with
J.J. Bevan.