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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.
Bernhard Lamel 《Journal of Geometric Analysis》2001,11(4):627-633
We give an invariant nondegeneracy condition for CR-maps between generic submanifolds in different dimensions and use it to
prove a reftection principle for these maps. 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.
Jiří Lebl 《Journal of Geometric Analysis》2007,17(2):321-341
A local uniqueness property of holomorphic functions on real-analytic nowhere minimal CR submanifolds of higher codimension
is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being
contained a possibly singular real-analytic Levi-flat hypersurface is studied and characterized. This question is completely
resolved for algebraic submanifolds of codimension 2 and a sufficient condition for noncontainment is given for non algebraic
submanifolds. As a consequence, an example of a submanifold of codimension 2, not biholomorphically equivalent to an algebraic
one, is given. We also investigate the structure of singularities of Levi-flat hypersurfaces. 相似文献
5.
We deduce global biholomorphic equivalence from local biholomorphic equivalence near boundary points in the class of generalized
pseudoellipsoids, extending local biholomorphisms to global ones. We discuss related results on holomorphic proper maps. 相似文献
6.
We construct automorphisms of
C
n
which map certain discrete sequences one onto another with prescribed finite jet at each point, thus solving a general Mittag-Leffler
interpolation problem for automorphisms. Under certain circumstances, this can be done while also approximating a given automorphism
on a compact set. 相似文献
7.
The authors prove that a proper monomial holomorphic mapping from the two-ball to the N-ball has degree at most 2N-3, and
that this result is sharp. The authors first show that certain group-invariant polynomials (related to Lucas polynomials)
achieve the bound. To establish the bound the authors introduce a graph-theoretic approach that requires determining the number
of sinks in a directed graph associated with the quotient polynomial. The proof also relies on a result of the first author
that expresses all proper polynomial holomorphic mappings between balls in terms of tensor products. 相似文献
8.
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
9.
We prove that a pseudoholomorphic diffeomorphism between two almost complex manifolds with boundaries satisfying some pseudoconvexity
type conditions cannot map a pseudoholomorphic disc in the boundary to a single point. This can be viewed as an almost complex
analogue of a well known theorem of J. E. Fornaess. 相似文献
10.
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
11.
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
12.
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
13.
We consider certain pseudoconvex domains in C
n+1 and show that if the automorphism group is noncompact, then the domain is equivalent to
for some integerm ≥ 1.
Communicated by Steven Krantz 相似文献
14.
Two versions of Rubio de Francia’s extrapolation theorem for multivariable operators of functions are obtained. One version
assumes an initial estimate with different weights in each space and implies boundedness on all products of Lebesgue spaces.
Another version assumes an initial estimate with the same weight but yields boundedness on a product of Lebesgue spaces whose
indices lie on a line. Applications are given in the context of multilinear Calderón-Zygmund operators. Vector-valued inequalities
are automatically obtained for them without developing a multilinear Banach-valued theory. A multilinear extension of the
Marcinkiewicz and Zygmund theorem on ℓ2-valued extensions of bounded linear operators is also obtained. 相似文献
15.
We present a characterization of the open unit ball in a separable infinite dimensional Hilbert space by the property of automorphism
orbits among the domains that are not necessarily bounded. This generalizes the recent work of Kim and Krantz [6]. Key new
features of this article include: a lower bound estimate of the Kobayashi metric and distance near a pluri-subharmonic peak
boundary point of the domains in Banach spaces, an effective localization argument, and an improvement of weak-type convergence
of sequences of biholomorphic mappings of domains in Banach spaces. 相似文献
16.
Let ƒ be a birational map of C
d
,and consider the degree complexity or asymptotic degree growth rate δ(ƒ) = limn → ∞ (deg(ƒn))1/n.We introduce a family of elementary maps, which have the form ƒ = L o J, where L is (invertible) linear, and J(x
1
−1
,..., xd) = (x
1
−1
,...,x
d
−1
.We develop a method of regularization and show how it can be used to compute δ for an elementary map. 相似文献
17.
Anna Siano 《Journal of Geometric Analysis》2007,17(3):547-557
We construct explicit supporting manifolds and local holomorphic peak functions as obstructions to the extendability of holomorphic
functions on a class of domains not necessarily pseudoconvex in CN, N >2. 相似文献
18.
Hidetaka Hamada 《Journal of Geometric Analysis》1998,8(3):441-446
The purpose of this paper is to prove that every proper holomorphic self-mapping of a Reinhardt domain Ω in
C
n
which is a generalization of a complex ellipsoid is biholomorphic. The main novelty of our result is that Ω is a domain in
C
n
such that it is allowed to have a boundary point at which the Levi determinant has infinite order of vanishing. 相似文献
19.
Jiaping Wang 《Journal of Geometric Analysis》1998,8(3):485-514
We consider the existence, uniqueness and convergence for the long time solution to the harmonic map heat equation between
two complete noncompact Riemannian manifolds, where the target manifold is assumed to have nonpositive curvature. As an application,
we solve the Dirichlet problem at infinity for proper harmonic maps between two hyperbolic manifolds for a class of boundary
maps. The boundary map under consideration has finite many points at which either it is not differentiable or has vanishing
energy density. 相似文献
20.
Recently McNeal proved, by analytic methods, that the D’Angelo type of a boundary point of a convex domain agrees with the
maximal order of contact of the boundary with complex lines. We give an elementary geometric proof and generalization of McNeal’s
theorem.
Communicated by Steven Krantz 相似文献