共查询到20条相似文献,搜索用时 15 毫秒
1.
We study the Bloch constant for Κ-quasiconformal holomorphic mappings of the unit ball B of C
n
. The final result we prove in this paper is: If f is a Κ-quasiconformal holomorphic mappig of B into C
n
such that det(f′(0)) = 1, then f(B) contains a schlicht ball of radius at least
where C
n
> 1 is a constant depending on n only, and as n→∞.
Received June 24, 1998, Accepted January 14, 1999 相似文献
2.
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
3.
Berit Stensones 《Journal of Geometric Analysis》1996,6(2):317-339
In this paper we shall construct proper holomorphic mappings from strictly pseudoconvex domains in Cn into the unit ball in CN which satisfy some regularity conditions up to the boundary. If we only require continuity of the map, but not more, then there is a large class of such maps (see [2], [3], and [5]). On the other hand, if F is Ck on the closure, k > N ? n + 1, then there is a very small class of such maps. In fact such F must be holomorphic across the boundary (see [1] and [4]). We are interested in maps F that are less than CN ? n + 1, but more than continuous on the closure. Namely, we want to find out if this is a very small or a large class. Our main result is as follows. Theorem, (a) Let ga < 1/6; then there exists an N = N(α, n) such that we can find a map F: Bn → BN that is proper, holomorphic, and Lipschitz α up to the boundary, but F is not holomorphic across the boundary. (b) If D is a general strictly pseudoconvex domain with C∞ -boundary in Cn, then we can find a map F: D → BN, N = N(α, n), that is proper, holomorphic, and Lipschitz α up to the boundary of D. To do part (a) of the theorem we only need to show that we can find a proper holomorphic map F = (f1, …, FN): Bn → BN that is Lipschitz α and fN(z) = c(1 - Z1)1/6 for some constant c > 0. With this we can in fact ensure that the map in (a) is at most Lipschitz 1/6 on the closure of Bn. 相似文献
4.
Let D be a domain in the n-dimensional Euclidean space Rn, n ≥ 2, and let E be a compact in D. The paper presents conditions on the compact E under which any homeomorphic mapping
f = D ∖ E → Rn can be extended to a continuous mapping f = D → Rˉn = Rn ⋃ {∞}. These conditions define the class of NCS-compacts, which, for n = 2, coincides with the class of topologically removable
compacts for conformal and quasiconformal mappings. Bibliography: 11 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 213–220. 相似文献
5.
György Gát 《数学学报(英文版)》2007,23(12):2269-2294
A highly celebrated problem in dyadic harmonic analysis is the pointwise convergence of
the Fejér (or (C, 1)) means of functions on unbounded Vilenkin groups. There are several papers of
the author of this paper concerning this. That is, we know the a.e. convergence σ
n
f → f (n → ∞)
for functions f ∈ L
p
, where p > 1 (Journal of Approximation Theory, 101(1), 1–36, (1999)) and also
the a.e. convergence σM
n
f → f (n → ∞) for functions f ∈ L
1 (Journal of Approximation Theory,
124(1), 25–43, (2003)). The aim of this paper is to prove the a.e. relation lim
n
→ σ
n
f = f for each
integrable function f on any rarely unbounded Vilenkin group. The concept of the rarely unbounded
Vilenkin group is discussed in the paper. Basically, it means that the generating sequence m may be
an unbounded one, but its "big elements" are not "too dense".
Research supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. M
36511/2001 and T 048780 相似文献
6.
We study the projection p: Md ? Bd{\pi : \mathcal{M}_d \rightarrow \mathcal{B}_d} which sends an affine conjugacy class of polynomial
f : \mathbbC ? \mathbbC{f : \mathbb{C} \rightarrow \mathbb{C}} to the holomorphic conjugacy class of the restriction of f to its basin of infinity. When Bd{\mathcal{B}_d} is equipped with a dynamically natural Gromov–Hausdorff topology, the map π becomes continuous and a homeomorphism on the shift locus. Our main result is that all fibers of π are connected. Consequently, quasiconformal and topological basin-of-infinity conjugacy classes are also connected. The key
ingredient in the proof is an analysis of model surfaces and model maps, branched covers between translation surfaces which
model the local behavior of a polynomial. 相似文献
7.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2009,61(7):1151-1157
The paper is devoted to investigations in the field of space mappings. We prove that open discrete mappings f ∈ W
1,n
loc such that their outer dilatation K
O
(x, f) belongs to L
n−1
loc and the measure of the set B
f
of branching points of f is equal to zero have finite length distortion. In other words, the images of almost all curves γ in the domain D under the considered mappings f : D → ℝ
n
, n ≥ 2, are locally rectifiable, f possesses the (N)-property with respect to length on γ, and, furthermore, the (N)-property also holds in the inverse direction for liftings of curves. The results obtained generalize the well-known Poletskii
lemma proved for quasiregular mappings. 相似文献
8.
E. S. Dubtsov 《Siberian Mathematical Journal》2009,50(6):998-1006
Denote by Hol(B
n
) the space of all holomorphic functions in the unit ball B
n
of ℂ
n
, n ≥ 1. Given g ∈ Hol(B
m
) and a holomorphic mapping φ: B
m
→ B
n
, put C
φ
g
f = g · (f ∘ φ) for f ∈ Hol(B
n
). We characterize those g and φ for which C
φ
g
is a bounded (or compact) operator from the growth space A
−log(B
n
) or A
−β
(B
n
), β > 0, to the weighted Bergman space A
α
p
(B
m
), 0 < p < ∞, α > −1. We obtain some generalizations of these results and study related integral operators. 相似文献
9.
Shanyu Ji 《Journal of Geometric Analysis》1994,4(2):159-177
A Nevanlinna-type inequality is proved for holomorphic mapf:C
m →M and for intersection of sections of a line bundle overM, in which the intersection may not be pure dimensional and the map may be degenerate.
Partial financial support was provided by the NSF under grant number DMS-8922760. 相似文献
10.
Abstract
Thom–Pontrjagin constructions are used to give a
computable necessary and sufficient condition for a homomorphism ϕ
: H
n
(L;Z) → H
n
(M;Z) to be realized by a map
f : M → L of degree k for closed (n − 1)-connected 2n-manifolds M and L,
n > 1. A corollary is that
each (n − 1)-connected
2n-manifold admits selfmaps
of degree larger than 1, n
> 1.
In the most interesting case of dimension 4, with the
additional surgery arguments we give a necessary and sufficient
condition for the existence of a degree k map from a closed orientable
4-manifold M to a closed
simply connected 4-manifold L
in terms of their intersection forms; in particular, there is a
map f :
M → L of degree 1 if and only if the
intersection form of L is
isomorphic to a direct summand of that of
M.
Both authors are supported by MSTC, NSFC. The
comments of F. Ding, J. Z. Pan, Y. Su and the referee enhance
the quality of the paper 相似文献
11.
Let X and Y be topological spaces such that an arbitrary mapping f: X → Y for which every preimage f
−1 (G) of a set G open in Y is an F
σ-set in X can be represented in the form of the pointwise limit of continuous mappings f
n
: X → Y. We study the problem of subspaces Z of the space Y for which the mappings f: X → Z possess the same property.
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 9, pp. 1189–1195, September, 2008. 相似文献
12.
Éric Amar 《Arkiv f?r Matematik》2000,38(1):1-20
LetB be the unit ball ofC
n
, I give necessary conditions on sequenceS of points inB to beH
∞(B) interpolating in term of aC
n
valued holomorphic function zero onS (a substitute for the interpolating Blaschke product).
These conditions are sufficient to prove that the sequenceS is interpolating for ∩
p>1
(B) and is also interpolating forH
p
(B) for 1≤p<∞. 相似文献
13.
In this paper we are concerned with solutions, in particular with the univalent solutions, of the Loewner differential equation associated with non-normalized subordination chains on the Euclidean unit ball B in ${\mathbb{C}^n}$ . We also give applications to univalence conditions and quasiconformal extensions to ${\mathbb{C}^n}$ of holomorphic mappings on B. Finally we consider the asymptotical case of these results. The results in this paper are complete generalizations to higher dimensions of well known results due to Becker. They improve and extend previous sufficient conditions for univalence and quasiconformal extension to ${\mathbb{C}^n}$ of holomorphic mappings on B. 相似文献
14.
Mark L. Agranovsky 《Journal d'Analyse Mathématique》2011,113(1):293-304
Let f ∈ C
ω
(∂B
n
), where B
n
is the unit ball of ℂ
n
. We prove that if a,b ? [`(B)] na,b \in {\overline B ^n}, a ≠ b, for every complex line L passing through one of a or b, the restricted function f|L ??Bnf{|_{L \cap \partial {B^n}}} has a holomorphic extention to the cross-section L∩B
n
, then f is the boundary value of a holomorphic function in B
n
. 相似文献
15.
Ifn>2 and iff is a locally quasiconformal mapping from the ballB
n= {x∈R
n:⋎x⋎<1} intoR
n ∪ {∞} thenf is injective inB
n (r)={x∈R
n:⋎x⋎ <r} wherer>0 depends only onn and the maximal dilatation off.
Supported in part by the Samuel Neaman Fund, Special Year in Complex Analysis, Technion, I.I.T., Haifa, Israel, 1975/76. 相似文献
16.
F. Tovena 《Geometriae Dedicata》2009,139(1):15-31
Let M be a smooth complex manifold, and S(⊂ M) be a compact irreducible subvariety with dim
C
S > 0. Let be given either a holomorphic map f : M → M with f
|S
= id
S
, f ≠ id
M
, or a holomorphic foliation on M: we describe an approach that can be applied to both map and foliation in order to obtain index theorems.
Partially supported by GNSAGA, Centro de Giorgi, M.U.R.S.T. 相似文献
17.
D. V. Gugnin 《Proceedings of the Steklov Institute of Mathematics》2009,266(1):59-90
We introduce and study polynomially dependent homomorphisms, which are special linear maps between associative algebras with
identity. The multiplicative structure is much involved in the definition of such homomorphisms (we consider only the case
of maps f: A → B with commutative B). The most important particular case of these maps are the Frobenius n-homomorphisms, which were introduced by V.M. Buchstaber and E.G. Rees in 1996–1997. A 1-homomorphism f: A → B is just an algebra homomorphism (the algebra B is commutative). A typical example of an n-homomorphism is given by the sum of n algebra homomorphisms, f = f
1 + ... + f
n
, f
i
: A → B, 1 ≤ i ≤ n. Another example is the trace of n × n matrices over a field R of characteristic zero, tr: M
n
(R) → R, and, more generally, the character of any n-dimensional representation, tr ρ: A → R, ρ: A → M
n
(R). The properties of n-homomorphisms (some of which were proved by Buchstaber and Rees under additional conditions) are derived, and a general theory
of polynomially dependent homomorphisms is developed. One of the main results of the paper is a uniqueness theorem, which
distinguishes the classes of n-homomorphisms among all polynomially dependent homomorphisms by a single natural completeness condition. As a topological
application of n-homomorphisms, we consider the theory of n-homomorphisms between commutative C*-algebras with identity. We prove that the norm of any such n-homomorphism is equal to n and describe the structure of all such n-homomorphisms, which generalizes the classical Gelfand transform (the case of n = 1). An interesting fact discovered is that the Gelfand transform, which is a functorial bijection between appropriate spaces
of maps, becomes a homeomorphism after considering natural topologies on these spaces. 相似文献
18.
Letf(z, t) be a subordination chain fort ∈ [0, α], α>0, on the Euclidean unit ballB inC
n. Assume thatf(z) =f(z, 0) is quasiconformal. In this paper, we give a sufficient condition forf to be extendible to a quasiconformal homeomorphism on a neighbourhood of
. We also show that, under this condition,f can be extended to a quasiconformal homeomorphism of
onto itself and give some applications.
Partially supported by Grant-in-Aid for Scientific Research (C) no. 14540195 from Japan Society for the Promotion of Science,
2004. 相似文献
19.
Laura DeMarco 《Mathematische Annalen》2003,326(1):43-73
Let L(f)=∫log∥Df∥dμ
f
denote the Lyapunov exponent of a rational map, f:P
1→P
1
. In this paper, we show that for any holomorphic family of rational maps {f
λ
:λX} of degree d>1, T(f)=dd
c
L(f
λ
) defines a natural, positive (1,1)-current on X supported exactly on the bifurcation locus of the family. The proof is based on the following potential-theoretic formula
for the Lyapunov exponent:
Here F:C
2
→C
2
is a homogeneous polynomial lift of f; ; G
F
is the escape rate function of F; and capK
F
is the homogeneous capacity of the filled Julia set of F. We show, in particular, that the capacity of K
F
is given explicitly by the formula
where Res(F) is the resultant of the polynomial coordinate functions of F.
We introduce the homogeneous capacity of compact, circled and pseudoconvex sets K⊂C
2 and show that the Levi measure (determined by the geometry of ∂K) is the unique equilibrium measure. Such K⊂C
2 correspond to metrics of non-negative curvature on P
1, and we obtain a variational characterization of curvature.
Received: 28 November 2001 / Revised version: 2 April 2002 /
Published online: 10 February 2003 相似文献
20.
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