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Estimates for the Connection Coefficients

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

Abstract

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
$$*\xi = - \xi *\,,\,*(*\xi ) = - \xi .$$

Keywords

Evolution Equation Tensor Field Riemann Tensor Gronwall Inequality Initial Layer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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