Plasticity of the unit ball of c and c0

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 ↗ ∞.

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Polynomial extreme elements of the closed unit ball ofH∞(B)

Complex Variables Theory and Application An International Journal ◽

10.1080/17476939408814730 ◽

1994 ◽

Vol 25 (1) ◽

pp. 49-56 ◽

Cited By ~ 1

Author(s):

John N. McDonald

Keyword(s):

Unit Ball ◽

Closed Unit Ball

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Homogeneously Polyanalytic Kernels on the Unit Ball and the Siegel Domain

Complex Analysis and Operator Theory ◽

10.1007/s11785-021-01145-z ◽

2021 ◽

Vol 15 (6) ◽

Author(s):

Christian Rene Leal-Pacheco ◽

Egor A. Maximenko ◽

Gerardo Ramos-Vazquez

Keyword(s):

Unit Ball ◽

Siegel Domain

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

Boundary Value Problems ◽

10.1186/s13661-020-01476-4 ◽

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.

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Kelvin-Möbius-Invariant Harmonic Function Spaces on the Real Unit Ball

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2021.125298 ◽

2021 ◽

pp. 125298

Author(s):

H. Turgay Kaptanoğlu ◽

A. Ersin Üreyen

Keyword(s):

Harmonic Function ◽

Unit Ball ◽

Function Spaces ◽

The Real

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

Symmetry ◽

10.3390/sym13071285 ◽

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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