# Geometric Analysis

Thursday, October 23, 2014 - 9:50am - 10:20am

Michael Holst (University of California, San Diego)

The Einstein constraints equations are of fundamental interest in mathematical physics in the study of Einstein's theory of general relativity. This coupled nonlinear elliptic system must also be solved in various forms for gravitational wave simulation. These equations have been studied intensively for half a century; they are a particular example of a critical exponent problem, further examples of which arise commonly in geometric analysis. In this lecture, we first present some new results that extend the known solution theory for the Einstein constraint equations.