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Erratum to “The Hölder continuous subsolution theorem for complex Hessian equations”
Amel Benali1; Ahmed Zeriahi2
1 University of Gabes, Faculty of Sciences of Gabes, LR17ES11, Mathematics and Applications 6072 Gabes, Tunisia
2 Institut de Mathématiques de Toulouse, Université de Toulouse, CNRS, UPS 118 route de Narbonne, 31062 Toulouse cedex 09, France
Journal de l’École polytechnique — Mathématiques, Volume 8 (2021), pp. 779-789.
corrects The Hölder continuous subsolution theorem for complex Hessian equations

The statement and the proof of Theorem B in [BZ20] are not complete, except when the boundary datum g vanishes identically. We give here the correct version of the statement as well as a complete proof.

L’énoncé et la preuve du théorème B dans [BZ20] ne sont pas complets, sauf dans le cas où la donnée au bord g s’annule identiquement. Nous donnons ici la version correcte de l’énoncé ainsi qu’une démonstration complète.

Received:
Accepted:
Published online:
DOI: 10.5802/jep.157
Classification: 31C45, 32U15, 32U40, 32W20, 35J96
Keywords: Complex Monge-Ampère equations, complex Hessian equations, Dirichlet problem, obstacle problems, maximal subextension, capacity.
Mot clés : Équations de Monge-Ampère complexes, équations hessienne complexes, problème de Dirichlet, problèmes d’obstacle, sous-extension maximale, capacités hessiennes

Amel Benali 1; Ahmed Zeriahi 2

1 University of Gabes, Faculty of Sciences of Gabes, LR17ES11, Mathematics and Applications 6072 Gabes, Tunisia
2 Institut de Mathématiques de Toulouse, Université de Toulouse, CNRS, UPS 118 route de Narbonne, 31062 Toulouse cedex 09, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {Erratum to {{\textquotedblleft}The} {H\"older} continuous subsolution theorem for complex {Hessian} equations{\textquotedblright}},
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Amel Benali; Ahmed Zeriahi. Erratum to “The Hölder continuous subsolution theorem for complex Hessian equations”. Journal de l’École polytechnique — Mathématiques, Volume 8 (2021), pp. 779-789. doi : 10.5802/jep.157. https://jep.centre-mersenne.org/articles/10.5802/jep.157/

[BZ20] A. Benali & A. Zeriahi - “The Hölder continuous subsolution theorem for complex Hessian equations”, J. Éc. polytech. Math. 7 (2020), p. 981-1007 | DOI | Zbl

[GKZ08] V. Guedj, S. Kolodziej & A. Zeriahi - “Hölder continuous solutions to Monge-Ampére equations”, Bull. London Math. Soc. 40 (2008) no. 6, p. 1070-1080 | DOI | Zbl

[Lu12] C. H. Lu - Équations hessiennes complexes, Ph. D. Thesis, Université de Toulouse 3, 2012 | theses.fr

[Ngu12] N. C. Nguyen - “Subsolution theorem for the complex Hessian equation”, Univ. Iagel. Acta Math. 50 (2012), p. 69-88 | MR | Zbl

[Zer20] A. Zeriahi - “Remarks on the modulus of continuity of subharmonic functions”, 2020 | arXiv

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