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arXiv · 1004.2938

Improved breakdown criterion for Einstein vacuum equations in CMC gauge

Qian Wang
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Abstract

Let $\M_*=\cup_{t\in [t_0, t_*)} Σ_t$ be a part of vacuum globally hyperbolic space-time $(\bM, \bg)$, foliated by constant mean curvature hypersurfaces $Σ_t$ with $t_0<t_*<0$. We show that the foliation can be extended beyond $t_*$ if the second fundamental form $k$ and the lapse function $n$ satisfy $$ \int_{t_0}^{t_*}(\|k\|_{L^\infty(Σ_t)}+\|\nab \log n\|_{L^\infty(Σ_t)}) dt <\infty. $$ This improves the existing breakdown criteria for Einstein vacuum equations.

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Qian Wang. 2010-04-17. Improved breakdown criterion for Einstein vacuum equations in CMC gauge. https://arxiv.org/abs/1004.2938

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