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Annales Henri Poincaré

, Volume 16, Issue 10, pp 2239–2264 | Cite as

Static Potentials on Asymptotically Flat Manifolds

  • Pengzi Miao
  • Luen-Fai TamEmail author
Article

Abstract

We consider the question whether a static potential on an asymptotically flat 3-manifold can have nonempty zero set which extends to the infinity. We prove that this does not occur if the metric is asymptotically Schwarzschild with nonzero mass. If the asymptotic assumption is relaxed to the usual assumption under which the total mass is defined, we prove that the static potential is unique up to scaling unless the manifold is flat. We also provide some discussion concerning the rigidity of complete asymptotically flat 3-manifolds without boundary that admit a static potential.

Keywords

Manifold Scalar Curvature Gaussian Curvature Static Potential Integral Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MiamiCoral GablesUSA
  2. 2.Department of Mathematics, The Institute of Mathematical SciencesThe Chinese University of Hong KongHong KongChina

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