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April 2007 Extremal discs and holomorphic extension from convex hypersurfaces
Luca Baracco, Alexander Tumanov, Giuseppe Zampieri
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Ark. Mat. 45(1): 1-13 (April 2007). DOI: 10.1007/s11512-006-0016-7

Abstract

Let D be a convex domain with smooth boundary in complex space and let f be a continuous function on the boundary of D. Suppose that f holomorphically extends to the extremal discs tangent to a convex subdomain of D. We prove that f holomorphically extends to D. The result partially answers a conjecture by Globevnik and Stout of 1991.

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Luca Baracco. Alexander Tumanov. Giuseppe Zampieri. "Extremal discs and holomorphic extension from convex hypersurfaces." Ark. Mat. 45 (1) 1 - 13, April 2007. https://doi.org/10.1007/s11512-006-0016-7

Information

Received: 15 September 2005; Revised: 3 June 2006; Published: April 2007
First available in Project Euclid: 31 January 2017

zbMATH: 1151.32005
MathSciNet: MR2312949
Digital Object Identifier: 10.1007/s11512-006-0016-7

Rights: 2006 © Institut Mittag-Leffler

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Vol.45 • No. 1 • April 2007
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