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Let us talk about Cauchy problem for the Einstein field equations on an [tex]n+1[/tex] manifold [tex](V,g)[/tex]. The initial data is a couple [tex](\gamma, K)[/tex] on a hypersurface [tex]\Sigma[/tex] of [tex]V[/tex].

Since then, the data [tex](\gamma, K)[/tex] must satisfy the Gauss-Codazzi equations which leads to the so-called constraint equations. The conformal method is now to apply to these constraint equations.

I would like to ask you what is the idea of the conformal method in studying Einstein fields equations. Why we split initial data and why we are able to do that? Note that Einstein field equations are hyperbolic equations.

Thank you very much.

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# The idea of the conformal method?

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