Date: November 4, 2011 Christina Sormani, CUNY GC and Lehman College
Title: The Positive Mass Theorem and the Intrinsic Flat Distance
The SchoenYau Positive Mass Theorem states that an asymptotically flat 3 manifold
with nonnegative scalar curvature has positive ADM mass unless the manifold is
Euclidean space. Here we examine sequences of such manifolds whose ADM mass is
approaching 0. We assume the sequences have no interior minimal surfaces although we
do allow them to have boundary if it is a minimal surface as is assumed in the
Penrose inequality. We conjecture that they converge to Euclidean space in the
pointed Intrinsic Flat sense for a well chosen sequence of points. The Intrinsic
Flat Distance, introduced in work with Stefan Wenger (UIC), can be estimated using
filling manifolds which allow one to control thin wells and small holes. Here we
present joint work with Dan Lee (CUNY) constructing such filling manifolds
explicitly and proving the conjecture in the rotationally symmetric case.
