Estimates for the Riemann Curvature Tensor

  • Sergiu Klainerman
  • Francesco Nicolò
Part of the Progress in Mathematical Physics book series (PMP, volume 25)


This chapter is devoted to the proof of Theorem M7 in terms of the fundamental quantities Q, \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{Q} \). These quantities can be expressed, according to (3.5.1), as weighted integrals of the null components of \(\hat L_0 R,\hat L_0 R,\hat L^2 _0 R,\hat L_0 \hat L_T R and \hat L_S \hat L_T R\)along the null hypersurfaces C(λ) and \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{C} \)(ν). We recall their explicit expressions:
$$\begin{gathered} Q(\lambda ,\nu ) = Q_1 (\lambda ,\nu ) + Q_2 (\lambda ,\nu ) \hfill \\ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{Q} (\lambda ,\nu ) = \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{Q} _1 (\lambda ,\nu ) + \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{Q} _2 (\lambda ,\nu ) \hfill \\ \end{gathered}$$




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Copyright information

© Birkhäuser Boston 2003

Authors and Affiliations

  • Sergiu Klainerman
    • 1
  • Francesco Nicolò
    • 2
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Dipartimento di Matematica, Facoltà di Scienze, M.F.N.Università degli studi di Roma “Tor Vergata”RomaItaly

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