Holomorphic extensions

The notions of hyperbolicity and tautness modulo an analytic subset of complex spaces are due to S. Kobayashi. Much attention has been given to these notions, and the results on this problem can be applied to many areas of mathematics, in particular to the extensions of holomorphic mappings. The main goal of this article is to give necessary and sufficient conditions on the hyperbolicity or tautness modulo an analytic subset of complex spaces.

10p tamynhan5 10-12-2020 12 2   Download

In this paper, we establish a second main theorem for holomorphic mappings from a disc (R) into Pn(C) and families of hyperplanes in subgeneral position. Our result is an extension the classical second main theorem of Cartan-Nochka and the second main theorem of Fujimoto.

9p tamynhan9 02-12-2020 10 3   Download

Let G be a connected, real, semisimple Lie group contained in its complexification GC , and let K be a maximal compact subgroup of G. We construct a KC -G double coset domain in GC , and we show that the action of G on the K-finite vectors of any irreducible unitary representation of G has a holomorphic extension to this domain. For the resultant holomorphic extension of K-finite matrix coefficients we obtain estimates of the singularities at the boundary, as well as majorant/minorant estimates along the boundary. ...

85p tuanloccuoi 04-01-2013 48 7   Download

A basic result in the theory of holomorphic functions of several complex variables is the following special case of the work of H. Cartan on the sheaf cohomology on Stein domains ([10], or see [14] or [16] for more modern treatments). Theorem 1.1. If V is an analytic variety in a domain of holomorphy Ω and if f is a holomorphic function on V , then there is a holomorphic function g in Ω such that g = f on V . The subject of this paper concerns an add-on to the structure considered in Theorem 1.1 which...

25p tuanloccuoi 04-01-2013 51 5   Download

Trong bài báo này, khái niệm về không gian và không gian Forelli Hartogs được đưa ra. Bất biến của không gian Hartogs và Forelli thông qua các tấm phủ holomorphic được thành lập. Hơn nữa, theo các giả định trên hlerity holomorphically lồi ¨ K, chúng tôi cho thấy ba loại sau đây của các không gian phức tạp: Hartogs mở rộng không gian holomorphic, không gian Hartogs và không gian có tài sản Forelli trùng.

11p phalinh21 01-09-2011 55 4   Download