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On L 2-Estimates for \(\bar{\partial}\) on a Pseudoconvex Domain in a Complete Kähler Manifold with Positive Holomorphic Bisectional Curvature

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Let Ω be a relatively compact pseudoconvex domain in a complete Kähler manifold X with positive holomorphic bisectional curvature. If Ω has positive inner reach and is defined by a plurisubharmonic function of class \(\mathcal{C}^{1}\), we generalize the existence of the Diederich–Fornaess exponent for the distance function to the boundary ∂Ω. This property allows us to prove L 2 estimates for the \(\bar{\partial}\) operator and regularity properties for the \(\bar{\partial}\)-Neumann operator.

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    Séverine Biard

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  1. Séverine Biard
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Correspondence to Séverine Biard.

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Communicated by Gennadi Henkin.

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Biard, S. On L 2-Estimates for \(\bar{\partial}\) on a Pseudoconvex Domain in a Complete Kähler Manifold with Positive Holomorphic Bisectional Curvature. J Geom Anal 24, 1583–1612 (2014). https://doi.org/10.1007/s12220-012-9386-1

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  • DOI: https://doi.org/10.1007/s12220-012-9386-1

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