ScalingStacks

Corollary 4.39 . [046Z]

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Corollary 4.39.

(Exponential decay to semiflat metric away from SS) In the situation of Theorem 4.38, for ℓ~≳1\tilde{\ell}\gtrsim 1 the deviation of ω−\omega_{-} from its zeroth Fourier mode ω¯−\overline{\omega}_{-} decays exponentially:

|ω−−ω¯−|≤CA−3/4νe−κ​ℓ~.|\omega_{-}-\overline{\omega}_{-}|\leq CA^{-3/4}\nu e^{-\kappa\tilde{\ell}}.

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