The resolution of the bounded L2 curvature conjecture in general relativity

Sergiu Klainerman; Igor Rodnianski; Jérémie Szeftel

The resolution of the bounded L² curvature conjecture in general relativity

Sergiu Klainerman, Igor Rodnianski, Jérémie Szeftel

Mathematics

Princeton University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This paper reports on the recent proof of the bounded L² curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the L²-norm of the curvature and a lower bound of the volume radius of the corresponding initial data set.

Original language	American English
Title of host publication	Invited Lectures
Editors	Sun Young Jang, Young Rock Kim, Dae-Woong Lee, Ikkwon Yie
Publisher	KYUNG MOON SA Co. Ltd.
Pages	895-913
Number of pages	19
ISBN (Electronic)	9788961058063
State	Published - 2014
Event	2014 International Congress of Mathematicans, ICM 2014 - Seoul, Korea, Republic of Duration: Aug 13 2014 → Aug 21 2014

Publication series

Name	Proceeding of the International Congress of Mathematicans, ICM 2014
Volume	3

Conference

Conference	2014 International Congress of Mathematicans, ICM 2014
Country/Territory	Korea, Republic of
City	Seoul
Period	8/13/14 → 8/21/14

ASJC Scopus subject areas

General Mathematics

Keywords

Bilinear estimates
Cauchy problem
Einstein equations
Null structure
Rough solutions

Cite this

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title = "The resolution of the bounded L2 curvature conjecture in general relativity",

abstract = "This paper reports on the recent proof of the bounded L2 curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the L2-norm of the curvature and a lower bound of the volume radius of the corresponding initial data set.",

keywords = "Bilinear estimates, Cauchy problem, Einstein equations, Null structure, Rough solutions",

author = "Sergiu Klainerman and Igor Rodnianski and J{\'e}r{\'e}mie Szeftel",

year = "2014",

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editor = "Jang, {Sun Young} and Kim, {Young Rock} and Dae-Woong Lee and Ikkwon Yie",

booktitle = "Invited Lectures",

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Klainerman, S , Rodnianski, I & Szeftel, J 2014, The resolution of the bounded L² curvature conjecture in general relativity. in SY Jang, YR Kim, D-W Lee & I Yie (eds), Invited Lectures. Proceeding of the International Congress of Mathematicans, ICM 2014, vol. 3, KYUNG MOON SA Co. Ltd., pp. 895-913, 2014 International Congress of Mathematicans, ICM 2014, Seoul, Korea, Republic of, 8/13/14.

The resolution of the bounded L² curvature conjecture in general relativity. / Klainerman, Sergiu ; Rodnianski, Igor; Szeftel, Jérémie.
Invited Lectures. ed. / Sun Young Jang; Young Rock Kim; Dae-Woong Lee; Ikkwon Yie. KYUNG MOON SA Co. Ltd., 2014. p. 895-913 (Proceeding of the International Congress of Mathematicans, ICM 2014; Vol. 3).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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KW - Rough solutions

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