Title: Positive scalar curvature on manifolds with boundary
Abstract:
Since work of Gromov and Lawson around 1980, we have known
(under favorable circumstances) necessary and sufficient conditions
for a closed manifold to admit a Riemannian metric of positive scalar
curvature, but not much was known about analogous results for
manifolds with boundary (and suitable boundary conditions). In joint
work with Shmuel Weinberger of the University of Chicago, we give
necessary and sufficient conditions in many cases for compact
manifolds with non-empty boundary to admit:
(a) a positive scalar
curvature metric which is a product metric in a neighborhood of the
boundary, or
(b) a positive scalar curvature metric with positive mean
curvature on the boundary.