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.
Extremal discs and the holomorphic extension from convex hypersurfaces
BARACCO, LUCA;ZAMPIERI, GIUSEPPE
2007
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.File in questo prodotto:
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ExtremalDiscsHolomorphicExtensionConvex(ArkMat07).pdf
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