Extremal discs and the holomorphic extension from convex hypersurfaces

Details Extremal discs and the holomorphic extension from convex hypersurfaces Extremal discs and the holomorphic extension from convex hypersurfaces

2005-05-07

arxiv.org/abs/math/0505122v1

Mathematics

Complex Variables

Scientific paper

10.1007/s11512-006-0016-7

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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