Extremal discs and the holomorphic extension from convex hypersurfaces
Complex Variables
2009-11-11 v1
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.
Cite
@article{arxiv.math/0505122,
title = {Extremal discs and the holomorphic extension from convex hypersurfaces},
author = {Luca Baracco and Alexander Tumanov and Giuseppe Zampieri},
journal= {arXiv preprint arXiv:math/0505122},
year = {2009}
}