J. M. Isidro
We prove that if $D\subset C^n$ is a bounded domain with real analytic boundary and D is pseudoconvex then the compact open topology in the group of holomorphic automorphisms of D is the topology of uniform convergence on D.
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In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.
We extend the difference analogue of Cartan's second main theorem for the case of slowly moving periodic hyperplanes, and introduce two different natural ways to find a difference analogue of the truncated second main theorem. As applications, we obtain a new Picard type theorem and difference analogues of the deficiency relation for holomorphic curves.
In this paper we prove Cartan theorems A and B for Stein manifolds over certain discrete valuation rings.
In this paper, we give some extension of fundamental theorems in Nevanlinna - Cartan theory for holomorphic curve on M punctured complex planes. As an application, we establish a result for uniqueness problem of holomorphic curve by inverse image of a hypersurface, it is improvement of some results before [8, 14] in this trend.
The possibility of reversion of the inequality in the Second Main Theorem of Cartan in the theory of holomorphic curves in projective space is discussed. A new version of this theorem is proved that becomes an asymptotic equality for a class of holomorphic curves defined by solutions of linear differential equations.
A converse of Cartan's Theorem B for Real Analytic Set
本文证明了由 Fernando 和 Ghiloni 提出的关于实解析集的 Cartan 定理 B 的逆定理。
We generalize the H. Cartan's theory of holomorphic curves for a general open Riemann surface. Besides, a vanishing theorem for jet differentials and a Bloch's theorem for Riemann surfaces are obtained.
This paper treats a holomorphic self-mapping f: Omega --> Omega of a bounded domain Omega in a separable Hilbert space H with a fixed point p. In case the domain is convex, we prove an infinite-dimensional version of the Cartan-Caratheodory-Kaup-Wu Theorem. This is basically a rigidity result in the vein of the uniqueness part of the classical Schwarz lemma. The main technique, inspired by an old idea of H. Cartan, is iteration of the mapping f and its derivative. A normality result for holomorphic mappings in the compact-weak-open topology, due to Kim and Krantz, is used.
In 1983, Nochka proved a conjecture of Cartan on defects of holomorphic curves in CP^n relative to a possibly degenerate set of hyperplanes. In this paper, we generalize the Nochka's theorem to the case of curves in a complex projective variety intersecting hypersurfaces in subgeneral position.
We establish basic results of complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds (such as algebras of Bohr's holomorphic almost periodic functions on tube domains or algebras of all fibrewise bounded holomorphic functions arising, e.g., in the corona problem for $H^\infty$). In particular, in this context we obtain results on holomorphic extension from complex submanifolds, properties of divisors, corona type theorems, holomorphic analogues of the Peter-Weyl approximation theorem, Hartogs type theorems, characterizations of uniqueness sets,…
Cartan uniqueness theorem on nonopen sets
本文研究非开集上的 Cartan 唯一性定理，通过解析圆盘包络条件建立全纯限制的唯一延拓，并推广至实解析子簇的无穷小 CR 自同构，证明圆形子簇的相关自同构必为线性。
We develop complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds. This, in particular, includes the results on holomorphic extension from complex submanifolds, corona type theorems, properties of divisors, holomorphic analogs of the Peter-Weyl approximation theorem, Hartogs type theorems, characterization of uniqueness sets. The model examples of these algebras are: (1) Bohr's algebra of holomorphic almost periodic functions on tube domains; (2) algebra of all fibrewise bounded holomorphic functions (e.g., arising in the corona problem for $H^…
Tropical Cartan's second main theorem for hyperplanes in general position
针对全纯曲线与一般位置超平面相交的情形，证明了热带Cartan第二主要定理的模拟，无需增长条件和例外集，并改进了先前结果。
Cartan-Thullen theorem and Levi problem in context of generalised convexity
本文在广义凸性框架下证明Cartan-Thullen定理与Levi问题可归为经典泛函分析定理的推论，并给出Stein空间的新刻画及Bremermann-Lelong引理与Levi问题的等价性。
For a domain $Ω$ in the complex plane, we consider the domain $S_n(Ω)$ consisting of those $n\times n$ complex matrices whose spectrum is contained in $Ω$. Given a holomorphic self-map $Ψ$ of $S_n(Ω)$ such that $Ψ(A)=A$ and the derivative of $Ψ$ at $A$ is identity for some $A\in S_n(Ω)$, we investigate when the map $Ψ$ would be spectrum-preserving. We prove that if the matrix $A$ is either diagonalizable or non-derogatory then for most domains $Ω$, $Ψ$ is spectrum-preserving on $S_n(Ω)$. Further, when $A$ is arbitrary, we prove that $Ψ$ is spectrum-preserving on a certain analytic subset of $S…
Cartan-Thullen theorem is a basic one in the theory of analytic functions of several complex variables. It states that for any open set $U$ of ${\mathbb C}^k$, the following conditions are equivalent: (a) $U$ is a domain of existence, (b) $U$ is a domain of holomorphy and (c) $U$ is holomorphically convex. On the other hand, when $f \, (\, =(f_1,f_2,\cdots,f_n)\, )$ is a $\mathbb C^n$-valued function on an open set $U$ of $\mathbb C^{k_1}\times\mathbb C^{k_2}\times\cdots\times\mathbb C^{k_n}$, $f$ is said to be $\mathbb C^n$-analytic, if $f$ is complex analytic and for any $i$ and $j$, $i\not=…
We investigate a class of actions of real Lie groups on complex spaces. Using moment map techniques we establish the existence of a quotient and a version of Luna's slice theorem as well as a version of the Hilbert-Mumford criterion. A global slice theorem is proved for proper actions. We give new proofs of results of Mostow on decompositions of groups and homogeneous spaces.
In this paper, we prove some fundamental theorems for holomorphic curves on angular domain intersecting a hypersurface, finite set of fixed hyperplanes in general position and finite set of fixed hypersurfaces in general position on complex projective variety with the level of truncation. As applications of the second main theorems for an angle, we will discuss the uniqueness problem of holomorphic curves in an angle instead of the whole complex plane. Detail, we establish a result for uniqueness problem of holomorphic curve by inverse image of a hypersurface. In my knowledge, this is the firs…
Vanishing of quaternionic cohomology groups and applications
研究轴对称域上切片正则函数的加法与乘法Cousin问题，利用四元数Cartan覆盖及分裂引理，从保切片函数与向量类函数的解推广至一般情形，证明相应上同调群消没，并给出射流插值定理及除子主性的应用。
Yan and Chen proved a weak Cartan-type second main theorem for holomorphic curves meeting hypersurfaces in projective space that included truncated counting functions. Here we give an explicit estimate for the level of truncation.
The modified Cartan conjecture
本文证明了修正的Cartan猜想在所有维度下成立，该猜想涉及单位圆盘到射影空间省略一般位置超平面的全纯曲线，并附带证明了Wronskian行列式零判定线性相关的定量版本。
A theorem due to Cartan asserts that every origin-preserving automorphism of bounded circular domains with respect to the origin is linear. In the present paper, by employing the theory of Bergman's representative domain, we prove that under certain circumstances Cartan's assertion remains true for quasi-circular domains in $\mathbb C^n$. Our main result is applied to obtain some simple criterions for the case $n=3$ and to prove that Braun-Kaup-Upmeier's theorem remains true for our class of quasi-circular domains.
By means of $C^\infty$-connections we will prove a general second main theorem and some special ones for holomorphic curves. The method gives a geometric proof of H. Cartan's second main theorem in 1933. By applying the same method, we will prove some second main theorems in the case of the product space $(\pone)^2$ of the Riemann sphere.
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