log-Hölder regularity of currents and equidistribution towards Green currents

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This is a Quantitative Study study.

Marco Vergamini

doi:10.48550/arxiv.2510.00789

October 1, 2025Open Access

log-Hölder regularity of currents and equidistribution towards Green currents

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Key Points

Pull-backs of currents converge exponentially to Green currents when iterated under endomorphisms.
This convergence is shown for observables that are log-Hölder continuous with bounded dd^c mass.
The research focuses on projective spaces and compact Kähler manifolds, highlighting rich geometric properties.
Key findings emphasize the significance of bounded mass in ensuring rapid convergence rates.

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Abstract

Let f be an endomorphism of a projective space or an automorphism of a compact Kähler 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-Hölder-continuous observables whose ddᶜ's have bounded mass.

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Marco Vergamini (2025) studied this question.

synapsesocial.com/papers/68e25378d6d66a53c2474228 https://doi.org/10.48550/arxiv.2510.00789

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log-Hölder regularity of currents and equidistribution towards Green currents

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log-Hölder regularity of currents and equidistribution towards Green currents

Key Points

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Abstract

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