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Extremal discs and holomorphic extension from convex hypersurfaces

Luca Baracco Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova Alexander Tumanov Department of Mathematics, University of Illinois Giuseppe Zampieri Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova

TBD mathscidoc:1701.333092

Arkiv for Matematik, 45, (1), 1-13, 2005.9
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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@inproceedings{luca2005extremal,
  title={Extremal discs and holomorphic extension from convex hypersurfaces},
  author={Luca Baracco, Alexander Tumanov, and Giuseppe Zampieri},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203618419874901},
  booktitle={Arkiv for Matematik},
  volume={45},
  number={1},
  pages={1-13},
  year={2005},
}
Luca Baracco, Alexander Tumanov, and Giuseppe Zampieri. Extremal discs and holomorphic extension from convex hypersurfaces. 2005. Vol. 45. In Arkiv for Matematik. pp.1-13. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203618419874901.
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