Convexity of Reduced Energy and Mass Angular Momentum Inequalities |
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Authors: | Richard Schoen Xin Zhou |
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Institution: | 1. Department of Mathematics, Stanford University, building 380, Stanford, California, 94305, USA
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Abstract: | In this paper, we extend the work in Chru?ciel and Costa (Class. Quant. Grav. 26:235013, 2009), Chru?ciel et al. (Ann. Phy. 323:2591–2613, 2008), Costa (J. Math. Theor. 43:285202, 2010), Dain (J. Diff. Geom. 79:33–67, 2008). We weaken the asymptotic conditions on the second fundamental form, and we also give an L 6?norm bound for the difference between general data and Extreme Kerr data or Extreme Kerr–Newman data by proving convexity of the renormalized Dirichlet energy when the target has non-positive curvature. In particular, we give the first proof of the strict mass/angular momentum/charge inequality for axisymmetric Einstein/Maxwell data which is not identical with the extreme Kerr–Newman solution. |
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