Fillins, extensions, scalar curvature, and quasilocal mass
Fillins, extensions, scalar curvature, and quasilocal mass

Christos Mantoulidis, Stanford University
Fine Hall 314
There is a special relationship between the Jacobi operator and the ambient scalar curvature operator, which we'll exploit. First, I'll talk about a "cutandfill" technique that simplifies 3manifolds of nonnegative scalar curvature. This was used in the study of a priori L^1 estimates for the boundary mean curvature of meanconvex fillins with nonnegative scalar curvature, and to generalize BrownYork mass. Second, I'll talk about an extremal bending technique that lets us compute the Bartnik mass of apparent horizons. Parts of this talk reflect work done jointly with R. Schoen/P. Miao.