Convexity of Reduced Energy and Mass Angular Momentum Inequalities
- 182 Downloads
In this paper, we extend the work in Chruściel and Costa (Class. Quant. Grav. 26:235013, 2009), Chruściel 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 L6−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.
Unable to display preview. Download preview PDF.
- 9.Evans L.: Partial Differential Equations. Graduate Studies in Mathematics, vol. 19. American Mathematical Society, Providence (1998)Google Scholar
- 10.Schoen, R.: Analytic Aspect of Harmonic Maps. In: ChernSeminar, S.S. (ed.) on Nonlinear PDE, MSRI Publication, pp. 321–358, Springer-Verlag, New York (1984)Google Scholar