Arkiv för Matematik

Extremal discs and holomorphic extension from convex hypersurfaces

Luca Baracco, Alexander Tumanov, and Giuseppe Zampieri

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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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Ark. Mat., Volume 45, Number 1 (2007), 1-13.

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

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2006 © Institut Mittag-Leffler


Baracco, Luca; Tumanov, Alexander; Zampieri, Giuseppe. Extremal discs and holomorphic extension from convex hypersurfaces. Ark. Mat. 45 (2007), no. 1, 1--13. doi:10.1007/s11512-006-0016-7.

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