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On the Bounded L2 Curvature Conjecture

On the Bounded L2 Curvature Conjecture

(p.224) Chapter Ten On the Bounded L2 Curvature Conjecture
Advances in Analysis
Sergiu Klainerman, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger
Princeton University Press

This chapter deals with a fundamental application of new methods to a geometric quasilinear equation to settle an important conjecture in General Relativity. According to the bounded curvature conjecture, the time of existence of a classical solution to the Einstein-vacuum equations depends only on the -norm of the curvature and a lower bound on the volume radius of the corresponding initial data set. At a deep level the curvature conjecture concerns the relationship between the curvature tensor and the causal geometry of an Einstein vacuum space-time. Thus, though the result is not optimal with respect to the standard scaling of the Einstein equations, it is nevertheless critical with respect to a different scaling tied to its causal properties.

Keywords:   geometric quasilinear equation, bounded L² curvature conjecture, General Relativity, Einstein-vacuum equations, Einstein equations, quasilinear hyperbolic system

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