Speaker
Richard Schoen, University of California Irvine
Abstract
Certain applications of minimal hypersurface theory to geometric problems work in all dimensions since the singularities which can occur in the hypersurfaces (in high dimensions) are sufficiently small that one can work on the regular set to obtain the conclusion. In applications to relativity this does not tend to be generally possible. This lecture will survey the regularity and singularity theory of minimal hypersurfaces and discuss results that can be extended to all dimensions and those which are still beyond current methods.