The Kobayashi metric in the normal direction and the mapping problem
Siqi Fu
利用Kobayashi度量在法线方向上的估计，研究了多复变数的映射问题。
Estimates of the Kobayashi metric in the normal direction are used to study the mapping problem in several complex variables.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We study extremal discs for the Kobayashi metric. Inspired by work of Lempert on strongly convex domains, we present results on strongly pseudoconvex domains. We also consider a useful biholomorphic invariant, inspired by the Kobayashi (and Carathéodory) metric, and prove several new results about biholomorphic equivalence of domains. Some useful results about automorphism groups of complex domains are also established.
In this paper, we construct a pseudoconvex domain in $\mathbb C^3$ where the Kobayashi metric does not blow up at a rate of one over distance to the boundary in the normal direction.
The Kobayashi metric for non-convex complex ellipsoids
本文给出了非凸复椭球中映射为$κ$ -测地线的必要条件。利用这些结果，我们明确地计算了Kobayashi度量在椭球$\{|z_1|^2+|z_2|^{2m}<1\}\subset\bold C^2$，其中$m<\frac12$。
The Schwarz lemma as one of the most influential results in complex analysis and it has a great impact to the development of several research fields, such as geometric function theory, hyperbolic geometry, complex dynamical systems, and theory of quasi-conformal mappings. In this note we mainly consider various version of Schwarz lemma and its relatives related to holomorphic functions including several variables.
We continue the research on the structure of complex geodesics in tube domains over (bounded) convex bases. In some special cases a more explicit form of the geodesics than the existing ones are provided. As one of the consequences of our study an effective formula for the Kobayashi-Royden metric in the tube domain $T_{\mathbb B_n}$ at the origin is given. The results on the Kobayashi-Royden metric in a natural way provide versions of the Schwarz Lemma for harmonic mappings. We also present a result on harmonic mappings defined on the disc that may be seen as a generalisation of the Radó-Knese…
This article considers isometries of the Kobayashi and Carathéod-ory metrics on domains in $ \mathbf{C}^n $ and the extent to which they behave like holomorphic mappings. First we prove a metric version of Poincaré's theorem about biholomorphic inequivalence of $ \mathbf{B}^n $, the unit ball in $ \mathbf{C}^n $ and $ Δ^n $, the unit polydisc in $ \mathbf{C}^n $ and then provide few examples which \textit{suggest} that $ \mathbf{B}^n $ cannot be mapped isometrically onto a product domain. In addition, we prove several results on continuous extension of isometries $ f : D_1 \rightarrow D_2 $ to…
Kobayashi-Hitchin Correspondence for Saturated Reflexive Parabolic Sheaves on Kähler manifolds
该工作利用 Hermitian-Yang-Mills 流，建立紧致 Kähler 流形上带简单正规交叉除子的饱和自反抛物层的 Kobayashi-Hitchin 对应。
A Hermitian metric on hyperbolic complex manifolds
本研究提出一种在Kobayashi双曲流形上定义Hermite度量的新方法，该度量在全纯映射下距离递减（相差乘法常数），区别于Wu的经典构造，有望具备更优的正则性。
Moebius transformations preserving fixed anharmonic ratio
O. Kobayashi在2007年证明了保非调和比的微分映射是Moebius变换。我们加强了他的结果，证明了可微性甚至内射性的要求可以省略。
Let $M$ be an $n$-dimensional complex manifold. A holomorphic function $f:M\to \mathbb C$ is said to be semi-Bloch if for every $λ\in \mathbb C$ the function $g_λ=\exp(λf(z))$ is normal on $M$. We characterise Semi-Bloch functions on infinitesimally Kobayashi non-degenerate $M$ in geometric as well as analytic terms. Moreover, we show that on such manifolds, semi-Bloch functions are normal.
Characterisation of geodesic-preserving functions
研究复域间全纯映射保持Kobayashi测地线的条件，刻画了单位圆盘和单位球中通过一点的测地线族下的保测地线映射。
In this paper, we present several necessary and sufficient conditions for a harmonic mapping to be normal. Also, we discuss maximum principle and five-point theorem for normal harmonic mappings. Furthermore, we investigate the convergence of sequences for sense-preserving normal harmonic mappings and show that the asymptotic values and angular limits are identical for normal harmonic mappings.
Results on normal harmonic and $φ$-normal harmonic mappings
本文研究平面调和映射中的正常性与$\phi$-正常性，建立Zalcman-Pang引理的调和映射版本，并引入扩展球面导数，给出$\phi$-正常的充分条件。
The main purpose of this paper is to study the concept of normal function in the context of harmonic mappings from the unit disk $\mathbb{D}$ to the complex plane. In particular, we obtain necessary conditions for that a function $f$ to be normal.
On normal families of quasiregular mappings
讨论了${\mathbb R}^n$中具有给定行为的拟亚纯映射在本质奇点邻域内的值分布。
A Zalcman-Pang type rescaling result for $ϕ$-normal harmonic mappings and applications
本文研究单位圆盘上调和映射的正规性与$ϕ$-正规性，建立涉及扩展球面导数的充分条件，证明Zalcman-Pang型重标度引理，并导出新的$ϕ$-正规性准则及Lappan型刻画。
In this article we prove a sufficient condition of quasi-normality in higher dimension for a family of meromorphic mappings in which each pair of functions of family shares some moving hypersurfaces. We also prove a normality criterion concerning shared moving hypersurfaces.
Normality criterion for logharmonic mapping
本文针对对数调和映射建立了正规性的充要条件，包括Marty准则、Zalcman-Pang引理和Lohwater-Pommerenke定理，并展示了引理的应用。
In this paper, we prove some results in normal family of meromorphic mappings intersecting with moving hypersurfaces. As some applications, we establish some results for normal mapping and extension of holomorphic mappings. A our result is strongly extended the Montel's normal criterion in the case several variables which is due to Tu in [Proc. Amer. Math. Soc. 127,1039-1049, 1999]. Our results are also strongly extended the results of Tu-Li in [Sci. China Ser. A. 48, 355-364, 2005] and [J. Math. Anal. Appl. 342, 629-638, 2006].
Lappan's five-point theorem for ϕ-Normal Harmonic Mappings
本文研究单位圆盘上调和映射的φ-正规性，给出若干充分条件，并将Lappan五点定理推广到φ-正规调和映射。
Let $\MSpace$ be a locally compact metric space and let $\pMap:\MSpace\to\MSpace$ be a not expansive map. We prove that for each $\ppa_0\in\MSpace$ the sequence $\ppa_0,\pMap(\ppa_0),\pMap^2(\ppa_0),\ldots$ is either relatively compact in $\MSpace$ or compactly divergent in $\MSpace$. As applications we study the structure of the functions which are limits of the iterates of the map $\pMap$ and we prove the analyticity of the set of $\pMap$-recurrent points when $\pMap:\MSpace\to\MSpace$ is a holomorphic and $\MSpace$ is a complex hyperbolic spaces in the sense of Kobayashi.
The Fekete-Szegö problem for starlike mappings of order $α$ and quasi-convex mappings of type $B$ in the unit balls of complex Banach spaces
该研究在复Banach空间单位球及ℂⁿ单位多圆盘上，针对两类全纯映射建立了广义Zalcman泛函与Fekete-Szegö不等式的精确估计，推广了经典结果并部分验证了高维广义Zalcman猜想。
Extension of Lohwater-Pommerenke's Theorem for strongly-normal Maps
引入全纯曲线和对数调和映射的强正规性概念，推广了Lohwater-Pommerenke关于非强正规映射的重标度刻画，并研究了Bloch映射和小Bloch映射的Zalcman-Pang型重标度结果，进一步扩展到强φ-正规映射。
We prove the existence of non-positively curved Kähler-Einstein metrics with cone singularities along a given simple normal crossing divisor on a compact Kähler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved Kähler-Einstein metrics with cone singularities. As an application we extend to this setting classical results of Lichnerowicz and Kobayashi on the parallelism and vanishing of appropriate holomorphic tensor fields.
The main aim of this article is to give some sufficient conditions for a family of meromorphic mappings on a domain D in C^n into P^N(C) to be meromorphically normal if they satisfy only some very weak conditions with respect to moving hypersurfaces in P^N(C), namely that their intersections with these moving hypersurfaces, which may moreover depend on the meromorphic maps, are in some sense uniform. Our results generalise and complete previous results in this area, especially the works of Fujimoto, Tu, Tu-Li, Mai-Thai-Trang and the recent work of Quang-Tan.
Normal forms and linearization of holomorphic dilation type semigroups in several variables
本文研究了$\mathbb{C}^n$中全纯映射的交换族，它们关于实参数构成交换半群。全纯映射的线性化模型是在Schröder经典函数方程的精神下使用的。
Quantum normal families: normal families of holomorphic functions and mappings on a Banach space
为研究无穷维赋范线性空间上的全纯函数和映射的正规族奠定了基础。正规族的特征，在值分布，球面导数，和其他几何性质的推导。建立了Montel型定理。考虑了全纯映射空间上的若干不同拓扑。关于正规族的定理用这些不同拓扑的语言来表述和证明。还介绍了正规函数。刻画方面的自同构，也在不变的衍生物。
Normality Criteria for Quasimeromorphic Mappings: Avoidance and Sharing
本文研究准共形映射的正常性，基于Lappan的正常映射理论，推导出在欧几里得空间中准共形映射的正常家族准则。
Beardon and Minda gave a characterization of normal families of holomorphic and meromorphic functions in terms of a locally uniform Lipschitz condition. Here, we generalize this viewpoint to families of mappings in higher dimensions that are locally uniformly continuous with respect to a given modulus of continuity. Our main application is to the normality of families of quasiregular mappings through a locally uniform Hölder condition. This provides a unified framework in which to consider families of quasiregular mappings, both recovering known results of Miniowitz, Vuorinen and others, and y…
We consider problems concerning the existence of solutions of the Beltrami equations and their convergence in the entire complex plane. We are mainly interested in the case when these solutions satisfy the so-called hydrodynamic normalization condition in the neighborhood of infinity. Under conditions related to dilations of inverse mappings, we have established the existence of such solutions in the class of continuous Sobolev mappings. We have also obtained results on the locally uniform limit of a sequence of such solutions.
Zalcman's lemma, Pinchuk's rescaling method, and Catlin's estimates revisited
本文提出一个统一的度量空间值映射重正规化引理，由此推导出 Zalcman 与 Miniowitz 经典引理，并为 C^2 中 Pinchuk 缩放方法建立一般正规性结论，重新证明了有限型域的 Catlin 估计。
Coefficient Problems for a Ma-Minda Convex Class Associated with the Normalized Arcsine Mapping
本文针对归一化反正切映射生成的Ma-Minda凸类，利用从属技巧等开展系数分析，得到泰勒系数、Hankel行列式等的精确估计，确定对应极值函数，证明所得不等式为最优。
The article is devoted to the study of mappings with finite distortion in metric spaces. Analogues of results relating to equicontinuity and normality of families of quasiregular mappings are obtained. It is proved that the indicated families are equicontinuous if the characteristic of the mappings has a finite mean oscillation at each inner point, and the maps omit a certain fixed continuum. An equicontinuity of generalized quasiisometries on Riemannian manifolds is also obtained.
Meromorphically normal families and a meromorphic Montel-Carathéodory theorem
本文研究了取值于 $\mathbb{P}^n$ 的亚纯映射族的亚纯正规性，受 Fujimoto 工作启发给出了一般充分条件，并据此建立了近期全纯映射正规族相关结果的亚纯类似物及 Montel-Carathéodory 定理的亚纯版本。
We study images of the unit ball under certain special classes of quasiregular mappings. For homeomorphic, i.e., quasiconformal mappings problems of this type have been studied extensively in the literature. In this paper we also consider non-homeomorphic quasiregular mappings. In particular, we study (topologically) closed quasiregular mappings originating from the work of J. Väisälä and M. Vuorinen in 1970's. Such mappings need not be one-to-one but they still share many properties of quasiconformal mappings. The global behavior of closed quasiregular mappings is similar to the local behavio…
Let $f(z)=h(z)+\overline{g(z)}$ be a harmonic mapping of the unit disk $U$. In this paper, the sharp coefficient estimates for bounded planar harmonic mappings are established, the sharp coefficient estimates for normalized planar harmonic mappings with $|h(z)|+|g(z)|\leq M$ are also provided. As their applications, Landau's theorems for certain biharmonic mappings are provided, which improve and refine the related results of earlier authors.
Propagation of analyticity for essentially finite C^infty-smooth CR mappings
利用解析圆盘的法向变形建立了解析几何反射原理。
It was shown by Kaup that every origin-preserving automorphism of quasi-circular domains is a polynomial mapping. In this paper, we study how the weight of quasi-circular domains and the degree of such automorphisms are related. By using the Bergman mapping, we prove that every origin-preserving automorphism of normal quasi-circular domains in $\mathbb C^2$ is linear.
On convergency properties of meromorphic functions and mappings
给出了亚纯函数和更一般的亚纯映射（强、弱、$Γ$ -收敛等）的几个不等价的收敛性概念.研究了它们之间的关系。给出了亚纯映射强收敛序列的Rouche定理的一个形式。进一步研究了亚纯映射族的正规集，与亚纯映射族的扩张性质的联系，以及亚纯映射族的体积的先验估计。最后，我们应用的技术开发的研究Fatou集的亚纯自同态的Kähler曲面。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。