ScalingStacks

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00SE

Theorem 4.23. (L∞L^{\infty}-estimate) The Calabi-Yau potential φC​Y,s\varphi_{CY,s} satisfies the uniform L∞L^{\infty}-estimate ‖φC​Y,s‖L∞≤C\left\lVert\varphi_{CY,s}\right\rVert_{L^{\infty}}\leq C.

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Proof. We apply Kolodziej’s estimate in Thm 2.7. The Skoda type inequality (2) is verified in Cor. 4.20, hence the L∞L^{\infty} estimate. ∎

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