On the Log-hyperconvexity Index of Pseudoconvex Hölder Domains in ℂⁿ

Abstract

In this note we prove that every bounded pseudoconvex domain in ℂⁿ with Hölder boundary admits a positive log-hyperconvexity index. We also get a better estimate for the plurisubharmonic exhaustion function.

Keywords

Pseudoconvex / hyperconvex / plurisubharmonic / 32T27

References

[1] ChenBY. Bergman kernel and hyperconvexity index. Anal. PDE, 2017, 10(6): 1429-1454.

[2] ChenBY. Every bounded pseudo-convex domain with Hölder boundary is hyperconvex. Bull. Lond. Math. Soc., 2021, 53(4): 1009-1015.

[3] ChenBY, XiongYP. A plurisubharmonic Hopf lemma for domains with cusp conditions. Ann. Polon. Math., 2022, 129(1): 1-15.

[4] Chen B.Y., Zheng Z.Y., Log-hyperconvexity index and Bergman kernel. Internat. J. Math., 2022, 33(12): Paper No. 2250081, 20 pp.

[5] ColtoiuM, MihalcheN. Pseudoconvex domains on complex spaces with singularities. Compositio Math., 1989, 72(3): 241-247

[6] DemaillyJ-P. Mesures de Monge–Ampère et mesures pluriharmoniques. Math. Z., 1987, 194(4): 519-564.

[7] DiederichK, FornæssJE. Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions. Invent. Math., 1977, 39(2): 129-141.

[8] HarringtonP. The order of plurisubharmonicity on pseudoconvex domains with Lipschitz boundaries. Math. Res. Lett., 2008, 15(3): 485-490.

[9] KerzmanN, RosayJ-P. Fonctions plurisousharmoniques d’exhaustion bornees et domaines taut. Math. Ann., 1981, 257(2): 171-184.

[10] RichbergR. Stetige streng pseudokonvexe Funktionen. Math. Ann., 1968, 175: 257-286.

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Peking University