Demetre Kazaras, Duke University
The spacetime Laplace equation on initial data sets for Einstein's equations
Abstract: This talk will consider a 'null spacetime Laplace'
operator on an initial data
set for the Einstein equations. This
operator reflects the geometry of the underlying
manifold in a manner
similar to the Dirac operator appearing in Witten's proof of the
Positive Mass Theorem. By analyzing linear-growth null spacetime
and their level sets, we obtain a rather
approachable refinement of the Positive Mass Theorem
asymptotically flat 3-dimensional initial data sets. Applications to
initial data sets are also considered. The
work I will discuss includes various collaborations with
Sven Hirsch, Marcus Khuri, Daniel Stern, and Yiyue Zhang.