arXiv subjects

Alexander Tumanov

Publications and source records attributed to Alexander Tumanov.

21 records · Page 2Linked to original sources

arXiv2005

Extremal discs and the 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.

math.CV↗

arXiv2002

A Morera type theorem in the strip

We prove the following result. Let f be a continuous function in the closed infinite strip in complex plane. Suppose the restriction of f to every circle inscribed in the strip extends holomorphically inside the circle. Then f is holomorphic in the open strip.

math.CV↗

arXiv2002

On the regularity of CR mappings in higher codimension

We give a proof of the regularity of Holder CR homeomorphisms of strictly pseudo convex CR manifolds of higher codimension.

math.CV↗