A global estimate for the Diederich--Fornaess index of weakly pseudoconvex domains

Abstract

A uniform upper bound for the Diederich--Fornaess index is given for weakly pseudoconvex domains whose Levi-form of the boundary vanishes in $\ell$-directions everywhere.

11 pages, final version, to appear in Nagoya Mathematical Journal

Cited by in corpus (12)

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• Curvature restrictions for Levi-flat real hypersurfaces in complex projective planes
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• The Diederich-Fornæss index I: for domains of non-trivial index
• On a hyperconvex manifold without non-constant bounded holomorphic functions
• The Diederich-Fornæss exponent and non-existence of Stein domains with Levi-flat boundaries
• The Diederich--Fornæss index and the regularities on the $\bar{\partial }$-Neumann problem
• The Diederich--Fornæss index II: for domains of trivial index
• On the dimension of the Bergman space for some unbounded domains
• Weakly 1-completeness of holomorphic fiber bundles over compact Kähler manifolds
• A CR proof for a global estimate of the Diederich--Fornaess index of Levi-flat real hypersurfaces
• The intrinsic geometry on bounded pseudoconvex domains