Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

An extension of H. Cartan's theorem

Author(s): So-chin Chen; Shih-Biau Jang
Journal: Proc. Amer. Math. Soc. 127 (1999), 2265-2271.
MSC (1991): Primary 32M05
Posted: March 23, 1999
MathSciNet review: 1618717
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: In this article we prove that if $D\subset \mathbb{C}^n$ , $n\ge 2$ , is a bounded pseudoconvex domain with real analytic boundary, then for each $g(z)\in \mathrm{Aut}(D)$ , there exists a fixed open neighborhood $\Omega _g$ of $\overline{D}$ and an open neighborhood of in $\mathrm{Aut}(D)$ such that any $h(z)\in V_g$ can be extended holomorphically to $\Omega _g$ , and that the action defined by

$\begin{align*}\pi:& V_g\times \Omega _g\to \mathbb{C}^n &(f,z)\mapsto \pi(f,z)=f(z) \end{align*}$

is real analytic in joint variables. This extends H. Cartan's theorem beyond the boundary. Some applications are also discussed here.

References:

1.: M.S.Baouendi, H.Jacobowitz and F.Treves, On the analyticity of mappings, Ann. of Math., 122 (1985), 365-400. MR 87f:32044
2.: D.Barrett, Regularity of the Bergman projection on domains with transverse symmetries, Math. Ann., 258 (1982), 441-446. MR 83i:32032
3.: E.Bedford, Action of the automorphisms of a smooth domain in ${\mathbb{C}}^{n}$ , Proc. Amer. Math. Soc., 93, (No.2) (1985), 232-234. MR 86e:32029
4.: E.Bedford and S.Pinchuk, Domains in ${\mathbb{C}}^{n+1}$ with noncompact automorphism group, J. of Geometric Analysis, 1, (No.3) (1991), 165-191. MR 92f:32024
5.: S.Bell, Weakly pseudoconvex domains with noncompact automorphism groups, Math. Ann., 280 (1988), 403-408. MR 89h:32052
6.: B.Coupet, Uniform extendibility of automorphisms, Contemporary Math. 137, Amer.
Math. Soc., (1992), 177-183. MR 93j:32033
7.: S.Krantz, Compactness principles in complex analysis, Seminarios I Volumen 3, Universidad autonóma de Madrid. División de Matematicas.
8.: D. Montgomery and L.Zippin, Topological transformation groups, Wiley-Interscience, New York (1955). MR 17:383b
9.: R.Narasimhan, Several complex variables, Univ. of Chicago Press, Chicago (1971). MR 49:7470
10.: A.G. Vitushkin, Holomorphic continuation of maps of compact hypersurfaces, Math. USSR t.2v., 20 (1983), 27-33.

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 32M05

Retrieve articles in all Journals with MSC (1991): 32M05

Additional Information:

So-chin Chen
Affiliation: Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan, Republic of China

Shih-Biau Jang
Affiliation: Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan, Republic of China

DOI: 10.1090/S0002-9939-99-04953-9
PII: S 0002-9939(99)04953-9
Keywords: Automorphism group, pseudoconvex domains, condition $R$
Received by editor(s): October 21, 1997
Posted: March 23, 1999
Additional Notes: Both authors are partially supported by a grant NSC 85-2121-M-007-028 from the National Science Council of the Republic of China.
Communicated by: Steven R. Bell
Copyright of article: Copyright 1999, American Mathematical Society

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|