Luca Baracco

Holomorphic extension from the sphere to the ball

Abstract Real analytic functions on the boundary of the sphere which have separate holomorphic extension along the complex lines through a boundary point have holomorphic extension to the ball. This was proved in Baracco (2009) [4] by an argument of CR geometry. We give here an elementary proof based on the expansion in holomorphic and antiholomorphic powers.

Extremal discs and holomorphic extension from convex hypersurfaces

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.

Erratum to: The range of the tangential Cauchy–Riemann system to a CR embedded manifold

We prove that every compact, pseudoconvex, orientable, CR manifold of

Separate real analyticity and CR extendibility

\C^n

Regularity at the boundary for v onQ-pseudoconvex domainsonQ-pseudoconvex domains

, bounds a complex manifold in the

The Boggess-Polking extension theorem forCR functions on manifolds with corners

C^\infty

Propagation of CR extendibility along complex tangent directions

sense. In particular, the tangential Cauchy-Riemann system has closed range.

Tangent discs and extension ofCR functions to wedges of ℂ n

Abstract It is proved here that a function in ℝ2 which is separately real analytic in one variable and CR extendible in the other (that is separately holomorphically extendible to a uniform strip), is real analytic. It is also considered the case when the CR extendibility occurs only on one side. The proof is obtained by bringing the problem into the frame of CR geometry.

Pseudoholomorphic Discs Attached to Pseudoconcave Domains

AbstractSolvability for