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June 2021 Smooth solutions to the complex plateau problem
Tommaso de Fernex
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J. Differential Geom. 118(2): 297-312 (June 2021). DOI: 10.4310/jdg/1622743141

Abstract

The paper builds on work of Du, Gao, and Yau. The main result provides a characterization of smooth solutions, up to normalization, of the complex Plateau problem for strongly pseudoconvex Calabi–Yau CR manifolds of dimension $2n - 1 \geq 5$ and in the hypersurface case when $n = 2$. The latter case was completely solved by Yau for $n \geq 3$ but only partially solved by Du and Yau for $n = 2$. As an application, we determine the existence of a link-theoretic invariant of normal isolated singularities that distinguishes smooth points from singular ones.

Funding Statement

Research partially supported by NSF Grant DMS-1700769.

Citation

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Tommaso de Fernex. "Smooth solutions to the complex plateau problem." J. Differential Geom. 118 (2) 297 - 312, June 2021. https://doi.org/10.4310/jdg/1622743141

Information

Received: 26 March 2018; Published: June 2021
First available in Project Euclid: 3 June 2021

Digital Object Identifier: 10.4310/jdg/1622743141

Subjects:
Primary: 32V99
Secondary: 32E10, 32S05

Rights: Copyright © 2021 Lehigh University

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Vol.118 • No. 2 • June 2021
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