Harmonic currents directed by foliations by Riemann surfaces

DOI10.1090/proc/15470zbMath1478.32100arXiv2010.03796OpenAlexW3123053555WikidataQ114094205 ScholiaQ114094205MaRDI QIDQ4992928

Hao Wu, Tien-Cuong Dinh

Publication date: 10 June 2021

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.03796

zbMATH Keywords

holomorphic foliationsLelong numberhyperbolic singularitydirected harmonic current

Mathematics Subject Classification ID

Singularities of holomorphic vector fields and foliations (32S65) Plurisubharmonic functions and generalizations (32U05)

Related Items (2)

Directed harmonic currents near non-hyperbolic linearizable singularities ⋮ Singular holomorphic foliations by curves. III: Zero Lelong numbers

Cites Work

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• Foliations, the ergodic theorem and Brownian motion
• Examples of minimal laminations and associated currents
• Cycles for the dynamical study of foliated manifolds and complex manifolds
• The \(\overline\partial\)-equation on a positive current
• Singular holomorphic foliations by curves. I: Integrability of holonomy cocycle in dimension 2
• Unique ergodicity for foliations in \(\mathbb {P}^2\) with an invariant curve
• Analyticity of sets associated to Lelong numbers and the extension of closed positive currents
• Unique ergodicity of harmonic currents on singular foliations of \({\mathbb{P}^2}\)
• Directed harmonic currents near hyperbolic singularities

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