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On the regularity of the Green current for semi-extremal endomorphisms of $ \mathbb{P}^2 $

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  • We study the regularity of the Green current for semi-extremal endomorphisms of $ \mathbb{P}^2 $. Under suitable assumptions, we show that the pointwise lower Radon-Nikodym derivative of stable slices with respect to the one dimensional Lebesgue measure is bounded at almost every point for the equilibrium measure. This provides a weak amount of metric regularity for the Green current along holomorphic discs.

    Mathematics Subject Classification: 37F10, 32U40, 28A15.

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