共查询到20条相似文献,搜索用时 15 毫秒
1.
Gong-ning Chen 《Journal of Mathematical Analysis and Applications》1985,112(1):274-278
Previous work (Gong-ning Chen, J. Math. Anal. Appl.98 (1984), 305–313) on iteration of holomorphic maps of Cn is continued. The purpose of this note is to extend results given in the above mentioned reference to the case of complex Hilbert spaces. Other comments are appended. 相似文献
2.
Jens Gravesen 《Acta Mathematica》1989,162(1):247-286
3.
Tetsuo Veda 《Journal of Geometric Analysis》1998,8(2):319-334
We study the dynamics of iterated holomorphic maps of a complex projective space onto itself. Relations between the Fatou
set and the orbits of critical points are investigated. In particular, results concerning critically finite maps on the Riemann
sphere are generalized to higher dimensional case. 相似文献
4.
Kentaro Ito 《Transactions of the American Mathematical Society》2008,360(7):3731-3749
The definition of the grafting operation for quasifuchsian groups is extended by Bromberg (preprint) to all -groups. In this paper, we show that the extended grafting maps behave as continuous maps for every sequence which converges ``standardly' to a boundary group, although the maps are not continuous in general. As a consequence of this result, we extend Goldman's grafting theorem for quasifuchsian groups to all boundary -groups.
5.
K. Wlodarczyk D. Klim E. Gontarek 《Proceedings of the American Mathematical Society》2000,128(12):3475-3482
Conditions guaranteeing the uniform convergence to constant maps of random iterations of holomorphic contractions on unbounded domains in complex Banach spaces are established.
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9.
For a Tychonoff space X, we use ↓USC(X) and ↓C(X) to denote the families of the regions below all upper semi-continuous maps and of the regions below all continuous maps from X to I=[0,1], respectively. In this paper, we consider the spaces ↓USC(X) and ↓C(X) topologized as subspaces of the hyperspace Cld(X×I) consisting of all non-empty closed sets in X×I endowed with the Vietoris topology. We shall prove that ↓USC(X) is homeomorphic (≈) to the Hilbert cube Q=ω[−1,1] if and only if X is an infinite compact metric space. And we shall prove that (↓USC(X),↓C(X))≈(Q,c0), where , if and only if ↓C(X)≈c0 if and only if X is a compact metric space and the set of isolated points is not dense in X. 相似文献
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11.
A generalization of Kwack's theorem to the infinite dimensional case is obtained. We consider a holomorphic map from into , where is a hypersurface in a complex Banach manifold and is a hyperbolic Banach space. Under various assumptions on , and we show that can be extended to a holomorphic map from into . Moreover, it is proved that an increasing union of pseudoconvex domains containing no complex lines has the Hartogs extension property.
12.
A map f:X→Y between topological spaces is defined to be scatteredly continuous if for each subspace AX the restriction f|A has a point of continuity. We show that for a function f:X→Y from a perfectly paracompact hereditarily Baire Preiss–Simon space X into a regular space Y the scattered continuity of f is equivalent to (i) the weak discontinuity (for each subset AX the set D(f|A) of discontinuity points of f|A is nowhere dense in A), (ii) the piecewise continuity (X can be written as a countable union of closed subsets on which f is continuous), (iii) the Gδ-measurability (the preimage of each open set is of type Gδ). Also under Martin Axiom, we construct a Gδ-measurable map f:X→Y between metrizable separable spaces, which is not piecewise continuous. This answers an old question of V. Vinokurov. 相似文献
13.
Zbigniew Slodkowski 《Journal of Geometric Analysis》1997,7(4):637-651
We consider an arbitrary real analytic family Xz,
, over the closed unit disc
, of real analytic plane Jordan curves Xz. Ifj
e
iθ
,e
iθ
∋ ∂D, is an arbitrary real-analytic family of orientation-reversing homeomorphisms of
fixingX
e
iθ
pointwise, we show that there is a unique holomorphic motion of
extending the given motion of Jordan curves and consistent with the given family of involutions. If these generalized reflections
are defined using the barycentric extension construction of Douady-Earle-Nag, then the resulting extension method for holomorphic
motions of X is natural, that is Moebius-invariant and continuous with respect to variation of the given motion of X0. 相似文献
14.
Lee Mosher 《Journal of Pure and Applied Algebra》1996,110(3):305-314
15.
Hanno Rund 《Annali di Matematica Pura ed Applicata》1972,93(1):99-110
Summary A special class of hypersurfaces of a Riemannian space is examined, this class being defined by the stipulation that the coefficients
of the third fundamental form be expressible as linear combinations of the coefficients of the first and second fundamental
forms. It is jound that these so-called C-hypersurfaces are umbilical provided that certain conditions (which may depend on
dimension) are satisfied. An (n-1)-dimensional Einstein space imbedded in an n-dimensional space of constant curvature is
such a C-hypersurface; accordingly the theory may be applied to the problem of the local imbedding of such spaces.
Entrata in Redazione il 23 giugno 1971. 相似文献
16.
A general Riesz merotopic space (X, ν) determines a not necessarily topological closure operator cν on X. The space (X, ν) is said to be complete if every cluster on (X, ν) is contained in an adherence grill on (X, cν). We discuss a method of obtaining a large class of completions of a given Riesz merotopic space with induced T1 closure space. As special cases we get the simple completion, which induces a simple closure space extension, and the strict completion, which induces a strict closure space extension. We show that the category of complete separated T1 Riesz merotopic spaces is epireflective in the category of separated T1 Riesz merotopic spaces, the reflection of an object being the simple completion. Similarly the category of complete clan-covered quasi-regular T1 Riesz merotopic spaces is epireflective in the category of clan-covered quasi-regular T1 Riesz merotopic spaces, the reflection of an object being the strict completion. 相似文献
17.
For a smooth functionf on ℝ
n
, we construct an extensionF to ℂ
n
with
vanishing to a high order on ℝ
n
and give precise estimates of how the degree of smothness is reflected in the degree of vanishing. This analysis is used
to define the
operator on (n,n−1) forms with singularities on ℝ
n
. 相似文献
18.
Neill Robertson 《manuscripta mathematica》1992,75(1):25-34
LetE andF be locally convex topological vector spaces. A holomorphic mapf: E→F is defined to be an Asplund map if it takes the separable subsets of a neighbourhood of eacha∈E into absolutely convex weakly metrisable subsets ofF; a Banach space is an Asplund space if and only if its identity map has this property. We show that a continuous linear map
from a quasinormable locally convex spaceE into a Banach spaceF is an Asplund map if and only if it factors through an Asplund space. IfE andF are both Banach spaces, then a holomorphic mapf: E→F is an Asplund map if and only if its derivative maps
factor through Asplund spaces for eacha∈E. This is true if and only if such a factorisation holds ata=0.
Part of this research was done during a visit to the University of Namibia, whose financial support is gratefully acknowledged
This article was processed by the author using the Springer-Verlag TEX mamath macro package 1990 相似文献
19.
Yuan Zhang 《Mathematische Annalen》2007,337(2):457-478
Let
and
denote the complexifications of Heisenberg hypersurfaces in
and
, respectively. We show that non-degenerate holomorphic Segre mappings from
into
with
possess a partial rigidity property. As an application, we prove that the holomorphic Segre non-transversality for a holomorphic Segre map from
into
with
propagates along Segre varieties. We also give an example showing that this propagation property of holomorphic Segre transversality fails when N > 2n − 2. 相似文献