Stability of the Positive Mass Theorem for Rotationally Symmetric Riemannian Manifolds

Details Stability of the Positive Mass Theorem for Rotationally Symmetric Riemannian Manifolds Stability of the Positive Mass Theorem for Rotationally Symmetric Riemannian Manifolds

2011-04-14

arxiv.org/abs/1104.2657v1

Mathematics

Differential Geometry

36 pages, 3 figures, open problems in the back

Scientific paper

We study the stability of the Positive Mass Theorem using the Intrinsic Flat Distance. In particular we consider the class of complete asymptotically flat rotationally symmetric Riemannian manifolds with nonnegative scalar curvature and no interior closed minimal surfaces whose boundaries are either outermost minimal hypersurfaces or are empty. We prove that a sequence of these manifolds whose ADM masses converge to zero must converge to Euclidean space in the pointed Intrinsic Flat sense. In fact we provide explicit bounds on the Intrinsic Flat Distance between annular regions in the manifold and annular regions in Euclidean space by constructing an explicit filling manifold and estimating its volume. In addition, we include a variety of propositions that can be used to estimate the Intrinsic Flat distance between Riemannian manifolds without rotationally symmetry. Conjectures regarding the Intrinsic Flat stability of the Positive Mass Theorem in the general case are proposed in the final section.

Affiliated with

Also associated with

No associations

Rating

Stability of the Positive Mass Theorem for Rotationally Symmetric Riemannian Manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stability of the Positive Mass Theorem for Rotationally Symmetric Riemannian Manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stability of the Positive Mass Theorem for Rotationally Symmetric Riemannian Manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-165162