Loewner chains and nonlinear resolvents of the Carathéodory family on the unit ball in Cn

2020 ◽  
Vol 491 (1) ◽  
pp. 124289
Author(s):  
Ian Graham ◽  
Hidetaka Hamada ◽  
Gabriela Kohr
Keyword(s):  
Unit Ball ◽  
Loewner Chains

scholarly journals Kernel convergence and biholomorphic mappings in several complex variables

2003 ◽  
Vol 2003 (67) ◽  
pp. 4229-4239 ◽  
Author(s):  
Gabriela Kohr
Keyword(s):  
Unit Ball ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Compact Sets ◽  
Growth Theorem ◽  
Convex Mappings ◽  
Loewner Chains ◽  
Kernel Convergence

We deal with kernel convergence of domains inℂnwhich are biholomorphically equivalent to the unit ballB. We also prove that there is an equivalence between the convergence on compact sets of biholomorphic mappings onB, which satisfy a growth theorem, and the kernel convergence. Moreover, we obtain certain consequences of this equivalence in the study of Loewner chains and of starlike and convex mappings onB.

scholarly journals General univalence criteria and quasiconformal extensions starting from Loewner chains theory

Filomat ◽  
2015 ◽  
Vol 29 (8) ◽  
pp. 1879-1892
Author(s):  
Paula Curt ◽  
Dorina Răducanu
Keyword(s):  
Unit Ball ◽  
Holomorphic Mappings ◽  
Quasiconformal Extension ◽  
Univalence Criterion ◽  
Loewner Chains ◽  
Dimensional Version ◽  
Univalence Criteria

The aim of this paper is to obtain general univalence conditions and quasiconformal extensions to Cn of holomorphic mappings defined on the Euclidian unit ball B. The asymptotical case of the quasiconformal extension results is also presented. We extend several results obtained by Hamada and Kohr(2011) in [15] to a more general case. In particular our results improve certain univalence criteria and quasiconformal extension results previously obtained by Pfaltzgraff [21], [22], Curt and Pascu [8], Curt [5], Hamada and Kohr [16], Curt and Kohr [6], [7] and R?ducanu [24]. As applications we present general forms of the n-dimensional version of the well-known univalence criterion due to Lewandowski [19] and its quasiconformal extension.

Holomorphically embedded discs with rapidly growing area

1999 ◽  
Vol 129 (2) ◽  
pp. 343-349
Author(s):  
Josip Globevnik
Keyword(s):  
Unit Ball ◽  
Open Unit ◽  
Open Unit Ball

It is shown that if V is a closed submanifold of the open unit ball of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ 1. It is also shown that if V is a closed submanifold of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ ∞.

scholarly journals Homogeneously Polyanalytic Kernels on the Unit Ball and the Siegel Domain

2021 ◽  
Vol 15 (6) ◽  
Author(s):  
Christian Rene Leal-Pacheco ◽  
Egor A. Maximenko ◽  
Gerardo Ramos-Vazquez
Keyword(s):  
Unit Ball ◽  
Siegel Domain

scholarly journals The exterior Dirichlet problems of Monge–Ampère equations in dimension two

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Limei Dai
Keyword(s):  
Asymptotic Behavior ◽  
Unit Ball ◽  
Bounded Domain ◽  
Viscosity Solutions ◽  
Sufficient Conditions ◽  
Radial Solutions ◽  
Dirichlet Problems ◽  
Necessary And Sufficient ◽  
Monge Ampere ◽  
Prescribed Asymptotic Behavior

AbstractIn this paper, we study the Monge–Ampère equations $\det D^{2}u=f$ det D 2 u = f in dimension two with f being a perturbation of $f_{0}$ f 0 at infinity. First, we obtain the necessary and sufficient conditions for the existence of radial solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a unit ball. Then, using the Perron method, we get the existence of viscosity solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a bounded domain.

scholarly journals Some Properties Concerning the JL(X) and YJ(X) Which Related to Some Special Inscribed Triangles of Unit Ball

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1285
Author(s):  
Asif Ahmad ◽  
Yuankang Fu ◽  
Yongjin Li
Keyword(s):  
Unit Ball ◽  
Banach Spaces ◽  
Uniformly Convex ◽  
Geometric Properties ◽  
James Constant ◽  
Von Neumann ◽  
Geometric Constants

In this paper, we will make some further discussions on the JL(X) and YJ(X) which are symmetric and related to the side lengths of some special inscribed triangles of the unit ball, and also introduce two new geometric constants L1(X,▵), L2(X,▵) which related to the perimeters of some special inscribed triangles of the unit ball. Firstly, we discuss the relations among JL(X), YJ(X) and some geometric properties of Banach spaces, including uniformly non-square and uniformly convex. It is worth noting that we point out that uniform non-square spaces can be characterized by the side lengths of some special inscribed triangles of unit ball. Secondly, we establish some inequalities for JL(X), YJ(X) and some significant geometric constants, including the James constant J(X) and the von Neumann-Jordan constant CNJ(X). Finally, we introduce the two new geometric constants L1(X,▵), L2(X,▵), and calculate the bounds of L1(X,▵) and L2(X,▵) as well as the values of L1(X,▵) and L2(X,▵) for two Banach spaces.

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