Communications in Mathematical Physics

, Volume 330, Issue 1, pp 33–43 | Cite as

A Gibbons–Penrose Inequality for Surfaces in Schwarzschild Spacetime

  • Simon Brendle
  • Mu-Tao WangEmail author


We propose a geometric inequality for two-dimensional spacelike surfaces in the Schwarzschild spacetime. This inequality implies the Penrose inequality for collapsing dust shells in general relativity, as proposed by Penrose and Gibbons. We prove that the inequality holds in several important cases.


Fundamental Form Minkowski Spacetime Curvature Vector Spacelike Hypersurface Null Hypersurface 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Department of MathematicsColumbia UniversityNew YorkUSA

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