On the Hartogs–bochner Phenomenon for Cr Functions in P2(c)
نویسنده
چکیده
Let M be a compact, connected, C2-smooth and globally minimal hypersurface M in P2(C) which divides the projective space into two connected parts U+ and U. We prove that there exists a side, U or U+, such that every continuous CR function on M extends holomorphically to this side. Our proof of this theorem is a simplification of a result originally due to F. Sarkis.
منابع مشابه
Hartogs Type Theorems for CR L functions on Coverings of Strongly Pseudoconvex Manifolds
We prove an analog of the classical Hartogs extension theorem for CR L2 functions defined on boundaries of certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a question formulated in the paper of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds.
متن کامل$L^p$ boundedness of the Bergman projection on some generalized Hartogs triangles
In this paper we investigate a two classes of domains in $mathbb{C}^n$ generalizing the Hartogs triangle. We prove optimal estimates for the mapping properties of the Bergman projection on these domains.
متن کاملMultiple Dirichlet Series and Automorphic Forms
This article gives an introduction to the multiple Dirichlet series arising from sums of twisted automorphic L-functions. We begin by explaining how such series arise from Rankin-Selberg constructions. Then more recent work, using Hartogs’ continuation principle as extended by Bochner in place of such constructions, is described. Applications to the nonvanishing of Lfunctions and to other probl...
متن کاملA Morse-theoretical Proof of the Hartogs Extension Theorem
100 years ago exactly, in 1906, Hartogs published a celebrated extension phenomenon (birth of Several Complex Variables), whose global counterpart was understood later: holomorphic functions in a connected neighborhood V(∂Ω) of a connected boundary ∂Ω b C (n > 2) do extend holomorphically and uniquely to the domain Ω. Martinelli in the early 1940’s and Ehrenpreis in 1961 obtained a rigorous pro...
متن کاملThe Bochner-Hartogs dichotomy for weakly 1-complete Kähler manifolds
© Annales de l’institut Fourier, 1997, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004