共查询到20条相似文献,搜索用时 531 毫秒
1.
Let M be a real analytic CR hypersurface in ℂ
n+1 admitting no varieties of positive dimension. We show first that every contracting local CR automorphism of M is linearizable. As a consequence, we show that such M admitting a contracting local CR automorphism is holomorphically equivalent to a weighted homogeneous hypersurface. Finally,
we apply these results to prove that a bounded domain in ℂ
n+1 with a real analytic boundary admitting an automorphism contracting at a boundary point must admit a Lie subgroup of real
dimension at least two in its automorphism group.
Research of the first named author is partially supported by The Grant R01-2005-000-10771-0 of The Korea Science and Engineering
Foundation. 相似文献
2.
Björn Ivarsson 《Arkiv f?r Matematik》2007,45(1):71-82
We describe the behavior of certain strictly plurisubharmonic functions near some real hypersurfaces in ℂ
n
, n≥3. Given a hypersurface we study continuous plurisubharmonic functions which are zero on the hypersurface and have Monge–Ampère
mass greater than one in a one-sided neighborhood of the hypersurface. If we can find complex curves which have sufficiently
high contact order with the hypersurface then the plurisubharmonic functions we study cannot be globally Lipschitz in the
one-sided neighborhood. 相似文献
3.
Effective algebraic degeneracy 总被引:1,自引:0,他引:1
We show that for every smooth projective hypersurface X⊂ℙ
n+1 of degree d and of arbitrary dimension n
≥2, if X is generic, then there exists a proper algebraic subvariety Y
⊊
X such that every nonconstant entire holomorphic curve f
:ℂ→X has image f(ℂ) which lies in Y, as soon as its degree satisfies the effective lower bound
d\geqslant 2n5d\geqslant 2^{n^{5}}
. 相似文献
4.
Nicolas Eisen 《Arkiv f?r Matematik》2012,50(1):69-87
We give a holomorphic extension result for continuous CR functions on a non-generic CR submanifold N of ℂ
n
to complex transversal wedges with edges containing N. We show that given any v∈ℂ
n
∖(T
p
N+iT
p
N), there exists a wedge of direction v whose edge contains a neighborhood of p in N, such that any continuous CR function defined locally near p extends holomorphically to that wedge. 相似文献
5.
Sylvain Damour 《manuscripta mathematica》2002,109(2):203-222
Let f : M → M′ be a smooth CR mapping between a generic real analytic submanifold M ⊂ ℂ
n
, n > 1, and a real analytic subset M′ ⊂ ℂ
n′
. We prove that if M is minimal and if M′ does not contain any complex curves, then f is analytic on a dense open subset of M. More generally, we establish an upper estimate of the partial analyticity of f, which depends on the maximal dimension of local holomorphic foliations contained in M
′
.
Received: 7 August 2001
Mathematics Subject Classification (2000): 32V25, 32V40, 32H99 相似文献
6.
We classify the germs of C¥\mathcal{C}^{\infty} CR manifolds that admit a smooth CR contraction. We show that such a CR manifold is embedded into ℂ
n
as a real hypersurface defined by a polynomial defining function consisting of monomials whose degrees are completely determined
by the extended resonances of the contraction. Furthermore, the contraction map extends to a holomorphic contraction that
coincides with its polynomial normal form. Consequently, several results concerning complex and CR geometry are derived. 相似文献
7.
Dejan Kolarič 《Journal d'Analyse Mathématique》2009,107(1):239-250
We investigate the notion of CR transversality of a generic holomorphic map f: ℂ
n
→ ℂ
m
to a smooth CR submanifold M of ℂ
m
. We construct a stratification of the set of non-CR transversal points in the preimage M′ = f
−1 (M) by smooth submanifolds, consisting of points where the CR dimension of M′ is constant. We show the existence of a Whitney stratification for sets which are locally diffeomorphic to the product of
an open set and an analytic set.
Work on this paper was supported by ARRS, Republic of Slovenia. 相似文献
8.
We give a Schwarz-Pick estimate for bounded holomorphic functions on unit ball in Cn, and generalize some early work of Schwarz-Pick estimates for bounded holomorphic functions on unit disk in C. 相似文献
9.
Abidi Jamel 《Rendiconti del Circolo Matematico di Palermo》2005,54(2):167-194
We prove the following result: If the function Max (log|ω -f
1(z)|, ..., log|ω -f
k(z)|) is plurisubharmonic in the open setD×ℂ (D open of ℂ
n
), thenf
1,...,f
k are analytic functions iff
1,...,f
k are continuous functions onD(k≥2). We prove also some other results. 相似文献
10.
11.
We prove the following Hartogs-Bochner type theorem: Let M be a connected C2 hypersurface of Pn(C) (n≥2) which divides Pn(C) in two connected open sets Ω1 and Ω2. Suppose that M has at most one open CR orbit. Then there exists i∈{1,2} such that C1 CR functions defined on M extends holomorphically to Ω
i
.
Supported by the TMR network. 相似文献
12.
We prove finite jet determination results for smooth CR embeddings, which are of constant degeneracy, using the method of
complete systems. As an application, we obtain a reflection principle for mappings between a Levinondegenerate hypersurface
in ℂ
N
and a Levinondegenerate hypersurface in ℂ
N+1.We also give an independent proof of the reflection principle for mappings between strictly pseudoconvex hypersurfaces in
any codimension due to Forstneric [14]. 相似文献
13.
Andrea F. Spiro 《Geometriae Dedicata》1997,67(2):199-221
Let M
2n+1
be an (abstract) smooth, real hypersurface of
n+1
, strongly pseudoconvex, and let us assume that there exists a non-compact CR transformation f fixing a point p M
2n+1
. We prove that there exists an f-contractible neighborhoodU of p (i.e. the closure of any orbit f
n
(u) with u U contains p). This gives an elementary proof of the following recent result by R. Schoen: a strongly pseudoconvex smooth real hypersurface in
2n+1
, admitting a non-compact transformation fixing a point, is globally equivalent to S
2n+1
or to S
2n+1
with a point deleted. 相似文献
14.
Christopher Hammond 《Journal of Geometric Analysis》2011,21(2):372-408
We derive Euler’s equation for the isoperimetric problem and the extremal hypersurface problem associated with Fefferman hypersurface
measure for strongly pseudoconvex real hypersurfaces in ℂ2. We use volume-preserving CR invariants to show that the only “torsion-free” solutions of Euler’s equation for the isoperimetric
problem are the volume-preserving images of spheres. 相似文献
15.
A. Bonilla F. Pérez-González A. Stray R. Trujillo-González 《Journal d'Analyse Mathématique》1997,73(1):65-89
This paper is concerned with several approximation problems in the weighted Hardy spacesH
p(Ω) of analytic functions in the open unit disc D of the complex plane ℂ. We prove that ifX is a relatively closed subset of D, the class of uniform limits onX of functions inH
p(Ω) coincides, moduloH
p(Ω), with the space of uniformly continuous functions on a certain hull ofX which are holomorphic on its interior. We also solve the simultaneous approximation problems of describing Farrell and Mergelyan
sets forH
p(Ω), giving geometric characterizations for them. By replacing approximating polynomials by polynomial multipliers of outer
functions, our results lead to characterizations of the same sets with respect to cyclic vectors in the classical Hardy spacesH
p(D), 1 ⪯p < ∞.
Dedicated to Professor Nácere Hayek on the occasion of his 75th birthday. 相似文献
16.
Sung-Yeon Kim 《Journal of Mathematical Analysis and Applications》2010,366(2):418-434
In this paper we show that a C∞ real hypersurface in Cn+1 of finite D'Angelo type admitting a weakly contracting local CR automorphism is CR equivalent to a weighted homogeneous hypersurface. As an application, we show that a bounded pseudoconvex domain in Cn+1 with C∞ boundary of finite D'Angelo type with a hyperbolic orbit accumulation point is biholomorphically equivalent to a domain defined by a weighted homogeneous polynomial. 相似文献
17.
Let G be a discrete subgroup of PU(1,n). Then G acts on ℙℂ
n
preserving the unit ball ℍℂ
n
, where it acts by isometries with respect to the Bergman metric. In this work we look at its action on all of ℙℂ
n
and determine its equicontinuity region Eq(G). This turns out to be the complement of the union of all complex projective hyperplanes in ℙℂ
n
which are tangent to ∂ℍℂ
n
at points in the Chen-Greenberg limit set Λ(G), a closed G-invariant subset of ∂ℍℂ
n
which is minimal for non-elementary groups. We also prove that the action on Eq(G) is discontinuous. Also , if the limit set is “sufficiently general” (i.e. it is not contained in any proper
k
-chain), then each connected component of Eq(G) is a holomorphy domain and it is a complete Kobayashi hyperbolic space. 相似文献
18.
Stanley M. Einstein-Matthews Clement H. Lutterodt 《Israel Journal of Mathematics》1999,109(1):253-271
LetX be a complete intersection algebraic variety of codimensionm>1 in ℂ
m+n
. We define the notion of (p,q)-order and (p,q)-K-type for transcendental entire functionsfεO(ℂ
m+n
) whereK is a non-pluripolar compact subset of ℂ
m+n
. Further, we consider the analogues of (p,q)-order and (p,q)-K-type inO(X). We discuss the series expansions of the functions inO(X) in terms of an orthogonal basis in a Hilbert spaceL
2(X, μ), where μ is a capacitary extremal measure onK.
Author is grateful to the NSA for partial support during the period of this research. 相似文献
19.
In this paper we consider special elements of the Fock space #x2131;
n
. That is the space of entire functionsf:ℂ:
n
→ℂ, such that the followingL
2- condition is satisfied:
. Here we show that there exists an entire functiong:ℂ
n
→ℂ such that for every one-dimensional subspace Π⊂ℂ
n
and for all 0<∈<2 we have
, but in the limit case ∈=0 we have
. This result is analogue to a result from [1]. There holomorphic functions on the unit-ball are investigated. Furthermore
the proof — as the one in [1] — uses a theorem from [2]. Therefore we give another application of the results from [2] — namely
for spaces of entire functions. 相似文献
20.
A new technique of integral representations in ℂ
n
, which is different from the well-known Henkin technique, is given. By means of this new technique, a new integral formula
for smooth functions and a new integral representation of solutions of the ∂-equations on strictly pseudoconvex domains in
ℂ
n
are obtained. These new formulas are simpler than the classical ones, especially the solutions of the ∂-equations admit simple
uniform estimates. Moreover, this new technique can be further applied to arbitrary bounded domains in ℂ
n
so that all corresponding formulas are simplified. 相似文献