共查询到20条相似文献,搜索用时 343 毫秒
1.
Baouendi M. S. Mir Nordine Rothschild Linda Preiss 《Journal of Geometric Analysis》2002,12(4):543-580
Results on finite determination and convergence of formal mappings between smooth generic submanifolds in ℂ
N
are established in this article. The finite determination result gibes sufficient conditions to guarantee that a formal map
is uniquely determined by its jet, of a preassigned order, at a point. Convergence of formal mappings for real-analytic generic
submanifolds under appropriate assumptions is proved, and natural geometric conditions are given to assure that if two germs
of such submanifolds are formally equivalent, then, they are necessarily biholomorphically equivalent. It is also shown that
if two real-algebraic hypersurfaces in ℂ
N
are biholomorphically equivalent, then, they are algebraically equivalent. All the results are first proved in the more general
context of “reflection ideals” associated to formal mappings between formal as well as real-analytic and real-algebraic manifolds. 相似文献
2.
Let ƒ: D → D′ be a proper holomorphic mapping between bounded domains D, D′ in ℂ2.Let M, M′ be open pieces on δD, δD′, respectively that are smooth, real analytic and of finite type. Suppose that the cluster
set of M under ƒ is contained in M′. It is shown that ƒ extends holomorphically across M. This can be viewed as a local version
of the Diederich-Pinchuk extension result for proper mappings in ℂ2. 相似文献
3.
We study whether the basin of attraction of a sequence of automorphisms of ℂ
k is biholomorphic to ℂ
k. In particular, we show that given any sequence of automorphisms with the same attracting fixed point, the basin is biholomorphic
to ℂ
k, if every map is iterated sufficiently many times. We also construct Fatou-Bieberbach domains in ℂ2
whose boundaries are four-dimensional. 相似文献
4.
Jörg Winkelmann 《Journal of Geometric Analysis》1998,8(2):335-340
We investigate the question whether a Mergelyan Theorem holds for mappings to ℂn ∖ A. The main result is the prove of such a theorem for mappings to ℂ2∖ℝ2. 相似文献
5.
In this paper, a class of biholomorphic mappings named quasi-convex mapping of order α in the unit ball of a complex Banach space is introduced. When the Banach space is confined to ℂ
n
, we obtain the relation between this class of mappings and the convex mappings. Furthermore, the growth and covering theorems
of this class of mappings are given on the unit ball of a complex Banach space X. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order
α defined on the polydisc in ℂ
n
and on the unit ball in a complex Banach space, respectively.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
6.
We consider holomorphic mappings sending a given Levi-nondegenerate pseudoconcave hypersurface M in Cn+1 into a nondegenerate hyperquadric of the same signature in PCN+1 and show that if M is sufficiently close to a hyperquadric in a certain sense, then any two such mappings differ only by an automorphism of the hyperquadric. 相似文献
7.
8.
A duality principle, relating the geometry of the Kobayashi metric with the CR geometry of the boundaries of smoothly bounded,
strongly convex domains in ℂ
n+1 is established. A characterization of the holomorphic Jacobi vector fields of those domains is also given. 相似文献
9.
A toral algebraic set A is an algebraic set in ℂ
n
whose intersection with T
n
is sufficiently large to determine the holomorphic functions on A. We develop the theory of these sets, and give a number
of applications to function theory in several variables and operator theoretic model theory. In particular, we show that the
uniqueness set for an extremal Pick problem on the bidisk is a toral algebraic set, that rational inner functions have zero
sets whose irreducible components are not toral, and that the model theory for a commuting pair of contractions with finite
defect lives naturally on a toral algebraic set. 相似文献
10.
Nordine Mir 《Mathematische Zeitschrift》1999,231(1):189-202
We give a new algebraic characterization of holomorphic nondegeneracy for embedded real algebraic hypersurfaces in , . We then use this criterion to prove the following result about real analyticity of smooth CR mappings: any smooth CR mapping
H between a real analytic hypersurface and a rigid polynomial holomorphically nondegenerate hypersurface is real analytic,
provided the map H is not totally degenerate in the sense of Baouendi and Rothschild.
Received September 19, 1997 相似文献
11.
Willem Veys 《manuscripta mathematica》1995,87(1):435-448
Tof ∈ℂ[x
1…,x
n
] one associates thetopological zeta function which is an invariant of (the germ of)f at 0, defined in terms of an embedded resolution of (the germ of)f
−1{0} inf
−1{0}. By definition the topological zeta function is a rational function in one variable, and it is related to Igusa’s local
zeta function. A major problem is the study of its poles.
In this paper we exactly determine all poles of the topological zeta function forn=2 and anyf ∈ℂ[x
1,x
2]. In particular there exists at most one pole of order two, and in this case it is the pole closest to the origin. Our proofs
rely on a new geometrical result which makes the embedded resolution graph of the germ off into an ‘ordered tree’ with respect to the so-callednumerical data of the resolution.
The author is a Postdoctoral Fellow of the Belgian National Fund for Scientific Research
N.F.W.O. 相似文献
12.
Andrew S. Raich 《Journal of Geometric Analysis》2006,16(2):353-374
We introduce classes of one-parameter families (OPF) of operators on C
c
t8
(ℂ) which characterize the behavior of operators associated to the
problem in the weighted space L2 (ℂ, e−2p) where p is a subharmonic, nonharmonic polynomial. We prove that an order 0 OPF operator extends to a bounded operator from
Lq (ℂ) to itself, 1 < q < ∞, with a bound that depends on q and the degree of p but not on the parameter τ or the coefficients
of p. Last, we show that there is a one-to-one correspondence given by the partial Fourier transform in τ between OPF operators
of order m ≤ 2 and nonisotropic smoothing (NIS) operators of order m ≤ 2 on polynomial models in ℂ2. 相似文献
13.
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
14.
15.
The main theorem of this article is a characterization of non compact simply connected complete Kobayashi hyperbolic complex
manifold of dimension n≽ 2 with real n
2-dimensional holomorphic automorphism group. Together with the earlier work [11, 12] and [13] of Isaev and Krantz, this yields
a complete classification of the simply-connected, complete Kobayashi hyperbolic manifolds with dimℝ Aut (M) ≽ (dimℂ
M)2. 相似文献
16.
Franc Forstneric 《Journal of Geometric Analysis》1999,9(1):93-117
Let n > 1 and let
C
n
denote the complex n-dimensional Euclidean space. We prove several jet-interpolation results for nowhere degenerate entire
mappings F:C
n →C
n
and for holomorphic automorphisms of
C
n
on discrete subsets of
C
n.We also prove an interpolation theorem for proper holomorphic embeddings of Stein manifolds into
C
n.For each closed complex submanifold (or subvariety) M ⊂
C
n
of complex dimension m < n we construct a domain Ω ⊂C
n
containing M and a biholomorphic map F: Ω →
C
n
onto
C
n
with J F ≡ 1such that F(M) intersects the image of any nondegenerate entire map G:C
n−m →C
n
at infinitely many points. If m = n − 1, we construct F as above such that
C
n ∖F(M) is hyperbolic. In particular, for each m ≥ 1we construct proper holomorphic embeddings F:C
m →C
m−1
such that the complement
C
m+1 ∖F(C
m
)is hyperbolic. 相似文献
17.
This work contains an improvement of earlier results of Boggess and Dwilewicz regarding global approximation of CR functions
by entire functions in the case of hypersurface graphs. In this work, we show that if ω, an open subset of a real hypersurface in ℂ
n
, can be graphed over a convex subset in ℝ2n−1, then ω is CR-Runge in the sense that continuous CR functions on ω can be approximated by entire functions on ℂ
n
in the compact open topology of ω. Examples are presented to show that this approximation result does not hold for graphed CR submanifolds in higher codimension.
R. Dwilewicz is partially supported by the Polish Science Foundation (KBN) grant N201 019 32/805. 相似文献
18.
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
19.
Let ƒ be a polynomial automorphism of ℂk of degree λ, whose rational extension to ℙk maps the hyperplane at infinity to a single point. Given any positive closed current S on ℙk of bidegree (1,1), we show that the sequence λ−n(ƒn)*S converges in the sense of currents on ℙk to a linear combination of the Green current T+ of ƒ and the current of integration along the hyperplane at infinity. We give an interpretation of the coefficients in terms
of generalized Lelong numbers with respect to an invariant dynamical current for ƒ−1. 相似文献
20.
We exhibit a collection of extreme points of the family of normalized convex mappings of the open unit ball of ℂ
n
forn≥2. These extreme points are defined in terms of the extreme points of a closed ball in the Banach space of homogeneous polynomials
of degree 2 in ℂ
n−1, which are fully classified. Two examples are given to show that there are more convex mappings than those contained in the
closed convex hull of the set of extreme points here exhibited. 相似文献