English

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.

Keywords

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}
}
R2 v1 2026-07-22T17:19:02.229Z