The Diederich–Fornæss Exponent and Non-existence of Stein Domains with Levi-Flat Boundaries

Siqi Fu; Mei Chi Shaw

doi:10.1007/s12220-014-9546-6

The Diederich–Fornæss Exponent and Non-existence of Stein Domains with Levi-Flat Boundaries

Siqi Fu, Mei Chi Shaw

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We study the Diederich–Fornæss exponent and relate it to non-existence of Stein domains with Levi-flat boundaries in complex manifolds. In particular, we prove that if the Diederich–Fornæss exponent of a smooth bounded Stein domain in an n-dimensional complex manifold is greater than k/n, then it has a boundary point at which the Levi-form has rank greater than or equal to k.

Original language	English (US)
Pages (from-to)	220-230
Number of pages	11
Journal	Journal of Geometric Analysis
Volume	26
Issue number	1
DOIs	https://doi.org/10.1007/s12220-014-9546-6
State	Published - Jan 1 2016

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Diederich–Fornaess exponent
Levi-flat hypersurface
Oka property
Stein manifold

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10.1007/s12220-014-9546-6

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abstract = "We study the Diederich–Forn{\ae}ss exponent and relate it to non-existence of Stein domains with Levi-flat boundaries in complex manifolds. In particular, we prove that if the Diederich–Forn{\ae}ss exponent of a smooth bounded Stein domain in an n-dimensional complex manifold is greater than k/n, then it has a boundary point at which the Levi-form has rank greater than or equal to k.",

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AU - Fu, Siqi

AU - Shaw, Mei Chi

N1 - Funding Information: This work was done while the first author visited the University of Notre Dame in April, 2012. He thanks the Department of Mathematics for the warm hospitality. The authors also thank the referee for constructive suggestions. The authors were supported in part by NSF Grants. Publisher Copyright: © 2014, Mathematica Josephina, Inc.

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N2 - We study the Diederich–Fornæss exponent and relate it to non-existence of Stein domains with Levi-flat boundaries in complex manifolds. In particular, we prove that if the Diederich–Fornæss exponent of a smooth bounded Stein domain in an n-dimensional complex manifold is greater than k/n, then it has a boundary point at which the Levi-form has rank greater than or equal to k.

AB - We study the Diederich–Fornæss exponent and relate it to non-existence of Stein domains with Levi-flat boundaries in complex manifolds. In particular, we prove that if the Diederich–Fornæss exponent of a smooth bounded Stein domain in an n-dimensional complex manifold is greater than k/n, then it has a boundary point at which the Levi-form has rank greater than or equal to k.

KW - Diederich–Fornaess exponent

KW - Levi-flat hypersurface

KW - Oka property

KW - Stein manifold

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The Diederich–Fornæss Exponent and Non-existence of Stein Domains with Levi-Flat Boundaries

Abstract

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