The causal structure of microlocalized rough Einstein metrics

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

This is the second in a series of three papers in which we initiate the study of very rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and Sobolev inequalities. In this paper we develop the geometric analysis of the Eikonal equation for microlocalized rough Einstein metrics. This is a crucial step in the derivation of the decay estimates needed in the first paper.

Original languageEnglish (US)
Pages (from-to)1195-1243
Number of pages49
JournalAnnals of Mathematics
Volume161
Issue number3
DOIs
StatePublished - May 1 2005

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Einstein Metrics
Rough
Eikonal Equation
Geometric Analysis
Sobolev Inequality
Decay Estimates
Energy Estimates
Albert Einstein
Initial Value Problem
Vacuum
Series
Energy
Decay

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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The causal structure of microlocalized rough Einstein metrics. / Klainerman, Sergiu; Rodnianski, Igor.

In: Annals of Mathematics, Vol. 161, No. 3, 01.05.2005, p. 1195-1243.

Research output: Contribution to journalArticle

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