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Advances in AnalysisThe Legacy of Elias M. Stein$
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Charles Fefferman, Alexandru D. Ionescu, D.H. Phong, and Stephen Wainger

Print publication date: 2014

Print ISBN-13: 9780691159416

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159416.001.0001

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PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 07 December 2021

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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