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arXiv · 2510.00789

$\log$-H\"older regularity of currents and equidistribution towards Green currents

Marco Vergamini
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Abstract

Let $f$ be an endomorphism of a projective space or an automorphism of a compact K\"ahler manifold. We prove that the pull-backs of currents under the iterates of $f$ converge exponentially fast to the Green currents when tested at $\log$-H\"older-continuous observables whose $\mathrm{dd^c}$'s have bounded mass.

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Marco Vergamini. 2025-10-01. $\log$-H\"older regularity of currents and equidistribution towards Green currents. https://arxiv.org/abs/2510.00789

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