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1.
Extension of proper holomorphic mappings past the boundary 总被引:2,自引:0,他引:2
It is proved that proper holomorphic mappings between n-dimensional bounded pseudoconvex domains with real analytic boundaries extend holomorphically past the boundary whenever the target domain is strictly pseudoconvex.Dedicated to Karl Stein 相似文献
2.
We show that if a bounded domain Ω is exhausted by a bounded strictly pseudoconvex domain D with C2 boundary, then Ω is holomorphically equivalent to D or the unit ball, and show that a bounded domain has to be holomorphically equivalent to the unit ball if its Fridman’s invariant has certain growth condition near the boundary. 相似文献
3.
Wei Wang 《Bulletin des Sciences Mathématiques》2011,(8):988-1010
Gaveau?s optimal control method for real and complex Monge–Ampere operators is generalized to that for quaternionic Monge–Ampere operator. It is also applied to investigate quaternionic regular functions: the characterization of the Silov boundary of a smooth quaternionic pseudoconvex domain. 相似文献
4.
Bernard Coupet Alexander Sukhov 《Proceedings of the American Mathematical Society》1996,124(11):3371-3380
We prove that a piecewise smoothly bounded strictly pseudoconvex domain with a non--compact automorphism group is biholomorphic to the ball. A boundary version of the Schwarz lemma for automorphisms of such a domain is settled.
5.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(7):597-602
We give an estimate for the distance functions related to the Bergman, Carathéodory, and Kobayashi metrics on a bounded strictly pseudoconvex domain with C2-smooth boundary. Our formula relates the distance function on the domain with the Carnot- Carathéodory metric on the boundary. As a corollary we conclude that the domain equipped with the any of the standard invariant distances is hyperbolic in the sense of Gromov. When the boundary of the domain is C3-smooth, our estimate is exact up to a fixed additive term. 相似文献
6.
Jiye Yu 《Proceedings of the American Mathematical Society》1997,125(8):2385-2390
We construct a smoothly bounded pseudoconvex domain whose boundary contains no complex analytic variety such that some boundary point admits no holomorphic peak function.
7.
Let D be a domain in ?2 such that the orbit of an internal point under the group Aut(D) of the holomorphic automorphisms of D accumulates to a smooth boundary point p. It is well known that if p is a strictly pseudoconvex point, such a local information forces D to be biholomorphic to the ball. We prove that if p is only weakly pseudoconvex of finite type, the domain D need not to be biholomorphic to a natural standard model. On the other end our results show that, under some convexity assumptions, D may be realized as a bounded domain with real analytic boundary except at most at one point. 相似文献
8.
9.
J. E. Fornæss posed the question whether the boundary point of smoothly bounded pseudoconvex domain is strictly pseudoconvex, when the asymptotic limit value of the squeezing function is 1. The purpose of this paper is to give an affirmative answer if the domain is in \(\mathbb {C}^{2}\) with smooth boundary of finite type in the sense of D’Angelo (Ann Math (2) 115(3):615–637, 1982). 相似文献
10.
Ding-dong Gong 《高校应用数学学报(英文版)》2008,23(3):273-278
Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the corresponding singular integral and a composition formula are obtained. This composition formula is quite different from usual ones in form. As an application, the corresponding singular integral equation and the system of singular integral equations are discussed as well. 相似文献
11.
《复变函数与椭圆型方程》2012,57(10):939-951
Let Ω be a bounded, weakly pseudoconvex domain in C n , n ≤ 2, with real-analytic boundary. A real-analytic submanifold M ? ?Ω is called an analytic interpolation manifold if every real-analytic function on M extends to a function belonging to (Ω¯). We provide sufficient conditions for M to be an analytic interpolation manifold. We give examples showing that neither of these conditions can be relaxed, as well as examples of analytic interpolation manifolds lying entirely within the set of weakly pseudoconvex points of ?Ω. 相似文献
12.
In this article we consider the complex Monge–Ampère equation with infinite boundary value in bounded pseudoconvex domains. We prove the existence of strictly plurisubharmonic solution to the problem in convex domains under suitable growth conditions. We also obtain, for general pseudoconvex domains, some nonexistence results which show that these growth conditions are nearly optimal. 相似文献
13.
R. Michael Range 《manuscripta mathematica》1977,20(4):309-313
Let D be a bounded domain with smooth boundary which is strictly pseudoconvex except at a finite number of points. It is shown that functions continuous on ¯D and holomorphic on D can be approximated uniformly on D by functions holomorphic on ¯D.Author partially supported by NSF grant MPS 75-07062. While carrying out this research, the author was a visitor at the University of Washington in Seattle. 相似文献
14.
15.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(11):1231-1236
Let Ω be a bounded, regular and pseudoconvex domain in ℂn, Ω, where ρ is plurisubharmonic and real analytic on ℂn − 1z. Then, if we suppose that ρ is strictly plurisubharmonic on ρ = 0, we have the global real analytic regularity of the ∂¯-Neumann problem on Ω for the (0, q)-forms. 相似文献
16.
J. M. Isidro 《Acta Mathematica Hungarica》2001,91(4):333-336
We prove that if D C is a bounded domain with real analytic boundary, and D is either pseudoconvex or it satisfies condition (R), then the compact open topology in Aut(D), the group of holomorphic automorphisms of D is the topology of uniform convergence on D. 相似文献
17.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(4):437-441
We define Nevanlinna classes in strictly pseudoconvex domains that are not necessarily smooth. If the boundary is defined by a Morse function we give sufficient conditions of Blaschke type for an analytic set to be the zero set of a function in a given Nevanlinna class. In particular, in the case of a smooth boundary we obtain new and rather explicit proofs of the theorems of Henkin-Skoda and Dautov-Henkin. 相似文献
18.
Burglind Jöricke 《Journal of Geometric Analysis》1999,9(2):257-300
Let Ω be a bounded strictly pseudoconvex domain in ℂn, n ≥ 3, with boundary ∂Ω, of class C2. A compact subset K is called removable if any analytic function in a suitable small neighborhood of ∂Ω K extends to an analytic
function in Ω. We obtain sufficient conditions for removability in geometric terms under the condition that K is contained
in a generic C2 -submanifold M of co-dimension one in ∂Ω. The result uses information on the global geometry of the decomposition of a CR-manifold
into CR-orbits, which may be of some independent interest. The minimal obstructions for removability contained in M are compact
sets K of two kinds. Either K is the boundary of a complex variety of co-dimension one in Ω or it is an exceptional minimal
CR-invariant subset of M, which is a certain analog of exceptional minimal sets in co-dimension one foliations. It is shown
by an example that the latter possibility may occur as a nonremovable singularity set.
Further examples show that the germ of envelopes of holomorphy of neighborhoods of ∞Ω K for K ⊂ M may be multisheeted. A couple
of open problems are discussed. 相似文献
19.
So-Chin Chen 《Inventiones Mathematicae》1988,92(1):173-185
In this paper we show that if \(D \subseteq \mathbb{C}^n ,n \geqq 2\) , is a smooth bounded pseudoconvex circular domain with real analytic defining functionr(z) such that \(\sum\limits_{k = 1}^n {z_k \frac{{\partial r}}{{\partial z_k }}} \ne 0\) for allz near the boundary, then the solutionu to the \(\bar \partial\) -Neumann problem, $$square u = (\bar \partial \bar \partial * + \bar \partial *\bar \partial )u = f,$$ is real analytic up to the boundary, if the given formf is real analytic up to the boundary. In particular, if \(D \subseteq \mathbb{C}^n ,n \geqq 2\) , is a smooth bounded complete Reinhardt pseudoconvex domain with real analytic boundary. Then ? is analytic hypoelliptic. 相似文献
20.
C~n中具有逐块光滑边界的有界域上带权因子积分表示的拓广式 总被引:5,自引:0,他引:5
本文讨论了Cn空间中具有逐块光滑边界的有界域上和强拟凸域上具有拓广的B-M核的(0,q)形式的带权因子的积分表示式,得到了带权因子拓广的Koppelman- Leray-Norguet公式.由此得到了有界域上-方程带权因子的连续解,由于权因子的引入,使得积分公式在应用上(如在函数插值问题的应用)具有更大的灵活性. 相似文献