Jump to ContentJump to Main Navigation
Advances in AnalysisThe Legacy of Elias M. Stein$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 26 February 2020

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

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.