共查询到20条相似文献,搜索用时 15 毫秒
1.
F. Colombo I. Sabadini D. C. Struppa A. Vajiac M. Vajiac 《Annali di Matematica Pura ed Applicata》2011,190(2):247-261
In this paper, we consider bicomplex holomorphic functions of several variables in
_boxclose C^n{{\mathbb B}{\mathbb C}^n} .We use the sheaf of these functions to define and study hyperfunctions as their relative 3n-cohomology classes. We show that such hyperfunctions are supported by the Euclidean space
\mathbb Rn{{\mathbb R}^n} within the bicomplex space
\mathbb B\mathbb Cn{{\mathbb B}{\mathbb C}^n}, and we construct an abstract Dolbeault complex that provides a fine resolution for the sheaves of bicomplex holomorphic
functions. As a corollary, we show how that the bicomplex hyperfunctions can be represented as classes of differential forms
of degree 3n − 1. 相似文献
2.
Barbara Visintin 《Annali di Matematica Pura ed Applicata》1999,177(1):263-276
We find explicitly all complex geodesics in a class of convex bounded Reinhardt domains ofC
n, which are a generalization of complex ellipsoids.
Entrata in Redazione il 19 maggio 1998. 相似文献
3.
4.
Irena Majcen 《Journal of Geometric Analysis》2009,19(3):695-707
We prove that certain infinitely connected domains D in a bordered Riemann surface, which admits a holomorphic embedding into C
2, admit a proper holomorphic embedding into C
2. We also prove that certain infinitely connected open subsets D⊂ℂ admit a proper holomorphic embedding into ℂ2.
相似文献
5.
In this note we determine the automorphism group of complex manifolds which are proper images of a simply connected strictly pseudoconvex domain in ?n. We also investigate automorphisms of domains invariant under a compact subgroup of complex linear transformations. Furthermore, some regularity and rigidity properties of proper holomorphic mappings are established. In particular we solve a question raised by Hahn and Pflug regarding the nonexistence of proper holomorphic mappings between the euclidian ball and the complex minimal ball of ?n. 相似文献
6.
We prove that every bordered Riemann surface admits a complete proper holomorphic immersion into a ball of $\mathbb C ^2$ , and a complete proper holomorphic embedding into a ball of $\mathbb C ^3$ . 相似文献
7.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(9):1063-1068
In this Note, we developp a new technic to study the existence of proper holomorphic mappings between a strictly pseudoconvex domain and certain special non-regular domains in ℂn. In particular, it can be applied in the case of the minimal ball and the Lie ball. We prove that self-proper holomorphic mappings between such domains are biholomorphic. Furthermore, we establish a necessary and sufficient condition to factorize a proper holomorphic mapping by automorphisms. Scaling method is applied for the first time in a singular points of the boundary of the domains. 相似文献
8.
Irena Majcen 《Arkiv f?r Matematik》2013,51(2):329-343
In this paper we consider proper holomorphic embeddings of finitely connected planar domains into ? n that approximate given proper embeddings on smooth curves. As a side result we obtain a tool for approximating a $\mathcal{C}^{\infty}$ diffeomorphism on a polynomially convex set in ? n by an automorphism of ? n that satisfies some additional properties along a real embedded curve. 相似文献
9.
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
10.
According to the Charzynski-Tammi conjecture, the symmetrized Pick function is extremal in the problem on the estimate for the nth Taylor coefficient in the class of holomorphic univalent functions close to the identical one. In this paper we find the exact value of M 4 such that the symmetrized Pick function is locally extremal in the problem on the estimate for the 4th Taylor coefficient in the class of holomorphic normalized univalent functions, whose module is bounded byM 4. 相似文献
11.
M. Grangé 《Archiv der Mathematik》2002,79(3):197-207
Let W \Omega be a convex open subset of \mathbbCn \mathbb{C}^n with cal C2 {cal C}^2 -boundary, and let a be a point in W \Omega . We prove that for a holomorphic function belonging to the Hardy class Hq(W) H^{q}(\Omega) , the Leibensons divisors at the point a are also in that class. 相似文献
12.
We describe all proper holomorphic mappings of the symmetrized polydisc and study its geometric properties. We also apply the obtained results to the study of the spectral unit ball in
Received: 8 June 2004 相似文献
13.
We define nonnegative quasi-nearly subharmonic functions on so called locally uniformly homogeneous spaces. We point out that
this function class is rather general. It includes quasi-nearly subharmonic (thus also subharmonic, quasisubharmonic and nearly
subharmonic) functions on domains of Euclidean spaces
\mathbbRn{{\mathbb{R}}^n}, n ≥ 2. In addition, quasi-nearly subharmonic functions with respect to various measures on domains of
\mathbbRn{{\mathbb{R}}^n}, n ≥ 2, are included. As examples we list the cases of the hyperbolic measure on the unit ball B
n
of
\mathbbRn{{\mathbb{R}}^n}, the M{{\mathcal{M}}}-invariant measure on the unit ball B
2n
of
\mathbbCn{{\mathbb{C}}^n}, n ≥ 1, and the quasihyperbolic measure on any domain
D ì \mathbbRn{D\subset {\mathbb{R}}^n},
D 1 \mathbbRn{D\ne {\mathbb{R}}^n}. Moreover, we show that if u is a quasi-nearly subharmonic function on a locally uniformly homogeneous space and the space satisfies a mild additional
condition, then also u
p
is quasi-nearly subharmonic for all p > 0. 相似文献
14.
We consider the convolution operators in spaces of functions which are holomorphic in a bounded convex domain in ℂ
n
and have a polynomial growth near its boundary. A characterization of the surjectivity of such operators on the class of
all domains is given in terms of low bounds of the Laplace transformation of analytic functionals defining the operators. 相似文献
15.
Wei Wang 《中国科学A辑(英文版)》2000,43(4):337-346
The estimate of a holomorphic supporting function for the generalized complex ellipsoid in ℂn is given, This domain is not decoupled. By using this estimate, the best possibleL
p estimates for the ∂-equation and some results of function theory on generalized complex ellipsoids are proved. 相似文献
16.
Let f be a non-invertible holomorphic endomorphism of
\mathbbPk{\mathbb{P}^{k}}, f
n
its iterate of order n and μ the equilibrium measure of f. We estimate the speed of convergence in the following known result. If a is a Zariski generic point in
\mathbbPk{\mathbb{P}^{k}}, the probability measures, equidistributed on the preimages of a under f
n
, converge to μ as n goes to infinity. 相似文献
17.
Maria Trybuła 《Archiv der Mathematik》2013,101(6):549-558
We consider proper holomorphic maps ${\pi : D\rightarrow G}$ , where D and G are domains in ${\mathbb{C}^{n}}$ . Let ${\alpha\in \mathcal{C}(G,\mathbb{R}_{ > 0})}$ . We show that every π induces some subspace H of ${\mathbb{A}^{2}_{\alpha\circ\pi}(D)}$ such that ${\mathbb{A}^{2}_{\alpha}(G)}$ is isometrically isomorphic to H via some unitary operator Γ. Using this isomorphism we construct the orthogonal projection onto H, and we derive Bell’s transformation formula for the weighted Bergman kernel function under proper holomorphic mappings. As a consequence of the formula, we get that the tetrablock is not a Lu Qi-Keng domain. 相似文献
18.
Suppose that Ω is a bounded domain with fractal boundary Γ in ${\mathbb R^{n+1}}Suppose that Ω is a bounded domain with fractal boundary Γ in
\mathbb Rn+1{\mathbb R^{n+1}} and let
\mathbb R0,n{\mathbb R_{0,n}} be the real Clifford algebra constructed over the quadratic space
\mathbb Rn{\mathbb R^{n}}. Furthermore, let U be a
\mathbb R0,n{\mathbb R_{0,n}}-valued function harmonic in Ω and H?lder-continuous up to Γ. By using a new Clifford Cauchy transform for Jordan domains
in
\mathbb Rn+1{\mathbb R^{n+1}} with fractal boundaries, we give necessary and sufficient conditions for the monogenicity of U in terms of its boundary value u = U|Γ. As a consequence, the results of Abreu Blaya et al. (Proceedings of the 6th International ISAAC Congress Ankara, 167–174,
World Scientific) are extended, which require Γ to be Ahlfors-David regular. 相似文献
19.
Romain Dujardin 《Geometric And Functional Analysis》2010,20(2):398-415
We give the first examples of positive closed currents T in ${{\mathbb C}^2}We give the first examples of positive closed currents T in
\mathbb C2{{\mathbb C}^2} with continuous potentials, T ùT = 0{T \wedge T = 0}, and whose supports do not contain any holomorphic disk. This gives in particular an affirmative answer to a question of
Forn?ss and Levenberg. We actually construct examples with potential of class C
1,α
for all α < 1. This regularity is expected to be essentially optimal. 相似文献
20.
We present a method for constructing global holomorphic peak functions from local holomorphic support functions for broad classes of unbounded domains in \(\mathbb {C}^n\). As an application, we establish a method for showing the positivity and completeness of invariant metrics including the Bergman metric mainly for the unbounded domains. 相似文献