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On the Bounded L2 Curvature Conjecture

On the Bounded L2 Curvature Conjecture

Chapter:
(p.224) Chapter Ten On the Bounded L2 Curvature Conjecture
Source:
Advances in Analysis
Author(s):
Sergiu Klainerman, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691159416.003.0010

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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