Extremal discs and the holomorphic extension from convex hypersurfaces

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.

Cited by in corpus (4)

• Complex dimensions of real manifolds, attached analytic discs and parametric argument principle
• Orthogonal testing families and holomorphic extension from the sphere to the ball
• Propagation of boundary CR foliations and Morera type theorems for manifolds with attached analytic discs
• Parametric argument principle and its applications to CR functions and manifolds