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arXiv · 1209.0019

Convexity of reduced energy and mass angular momentum inequalities

Richard Schoen·Xin Zhou
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Abstract

In this paper, we extend the work in \cite{D}\cite{ChrusLiWe}\cite{ChrusCo}\cite{Co}. 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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Richard Schoen, Xin Zhou. 2012-08-31. Convexity of reduced energy and mass angular momentum inequalities. https://doi.org/10.1007/s00023-013-0240-1

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