Estimates for the Connection Coefficients

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


We consider Hodge systems of equations defined on a compact two-dimensional Riemann surface. We recall Definition 3.1.4 of Chapter 3.

Definition 3.1.4 Given the 1-form ξ on S we define its Hodge dual 1
$${}^*\xi _a = \in _{ab} \xi ^b .$$
Clearly *(*ξ) = -ξ. If ξis a symmetric traceless 2-tensor, we define the following left, *ξ and right, ξ*, Hodge duals
$$^*\xi _{ab} = \in _{ab} \xi ^c \,b,\,\,\xi _{ab}^* = \xi _a ^c \in _{cb} .$$
Observe that the tensors *ξ,ξ* are also symmetric traceless and satisfy
$$*\xi = - \xi *\,,\,*(*\xi ) = - \xi .$$


Evolution Equation Tensor Field Riemann Tensor Gronwall Inequality Initial Layer 
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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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