Stability of the positive mass theorem for rotationally symmetric Riemannian manifolds
-
Dan A. Lee
and
Christina Sormani
Abstract.
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.
© 2014 by Walter de Gruyter Berlin Boston
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- Heegner cycles and derivatives of p-adic L-functions
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Articles in the same Issue
- Masthead
- Constant mean curvature surfaces in hyperbolic 3-space via loop groups
- La formule des traces pour les revêtements de groupes réductifs connexes. I. Le développement géométrique fin
- Heegner cycles and derivatives of p-adic L-functions
- On Chow motives of surfaces
- The locus of real multiplication and the Schottky locus
- Stability of the positive mass theorem for rotationally symmetric Riemannian manifolds
- Real trigonal curves and real elliptic surfaces of type I
