Complex Analysis and its Synergies

Bappaditya Bhowmik

Goutam Satpati

Criteria for quasiconformal extensions of harmonic mappings

调和映射拟共形延拓的准则

Abstract Let $$\Omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Ω</mml:mi> </mml:math> be a subdomain of a Stein surface with smooth strictly pseudoconvex boundary $$M=\partial \Omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>=</mml:mo> <mml:mi>∂</mml:mi> <mml:mi>Ω</mml:mi> </mml:mrow> </mml:math> . We are mainly interested in the case that $$\Omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Ω</mml:mi> </mml:math> is not relatively compact. Building on work by G. Lupacciolu, we describe the envelope of holomorphy of an arbitrary open subset $$M^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>M</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> of M in terms of a modified holomorphic hull of the complement $$A=M\backslash M^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>=</mml:mo> <mml:mi>M</mml:mi> <mml:mo>\</mml:mo> </mml:mrow> <mml:msup> <mml:mi>M</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:math> , designed in order to also reflect the geometry of $$\Omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Ω</mml:mi> </mml:math> at infinity. As a consequence, we clarify the relation between the envelope of $$M^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>M</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> and some notions of core sets of $$\Omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Ω</mml:mi> </mml:math> , which are an active topic in recent research.

Egmont Porten

Holomorphic extension in unbounded subdomains of Stein surfaces

Stein曲面无界子区域中的全纯延拓

Abstract Curve shortening in the z -plane in which, at a given point on the curve, the normal velocity of the curve is equal to the curvature, is shown to satisfy $$S_tS_z=S_{zz}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>z</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mrow> <mml:mi>zz</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , where S ( z , t ) is the Schwarz function of the curve. This equation is shown to have a parametric solution from which the known explicit solutions for curve shortening flow; the circle, grim reaper, paperclip and hairclip, can be recovered.

N. R. McDonald

The fundamental solutions of the curve shortening problem via the Schwarz function

通过Schwarz函数求解曲线缩短问题的基本解

We present an analytical proof that certain natural metric universal covers are Hadamard metric spaces. If $$\rho \,\mathrm{{d}}s$$ induces a complete distance d on a plane domain $$\Omega $$ , and $$\rho =\varphi \circ u$$ where u is (locally Lipschitz and) subharmonic in $$\Omega $$ , $$\varphi $$ is positive and increasing on an interval containing $$u(\Omega )$$ with $$\log \varphi $$ convex, then $$(\Omega ,d)$$ has a universal cover $$({\tilde{\Omega }},{\tilde{d}})$$ which is a Hadamard metric space (with geodesics that have Lipschitz continuous first derivatives).

David A. Herron

Gaven J. Martin

Subharmonic functions, conformal metrics, and CAT(0)

次调和函数，共形度量，及CAT(0)

John P. D’Angelo

Symmetries, rational sphere maps, and complete polynomial sequences

对称性、有理球面映射及完全多项式序列

Sofía Ortega Castillo

Strong pseudoconvexity in Banach spaces

巴拿赫空间中的强伪凸性

Jasbir Parashar

Anbareeswaran Sairam Kaliraj

On meromorphic harmonic functions with a pole at the origin

关于在原点具有极点的亚纯调和函数

Aijaz Bhat

Naseer Wani

N. A. Rather

On the derivatives of a polynomial with restricted zeros

关于具有受限零点的多项式的导数

Publication Information	Publisher: Springer International Publishing AG，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2015，Proportion of original research papers: ，Self Citation Rate:， Gold OA Rate:

Complex Analysis and its Synergies

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Criteria for quasiconformal extensions of harmonic mappings

Holomorphic extension in unbounded subdomains of Stein surfaces

The fundamental solutions of the curve shortening problem via the Schwarz function

Subharmonic functions, conformal metrics, and CAT(0)

Symmetries, rational sphere maps, and complete polynomial sequences

Criteria for quasiconformal extensions of harmonic mappings

Holomorphic extension in unbounded subdomains of Stein surfaces

Strong pseudoconvexity in Banach spaces

On meromorphic harmonic functions with a pole at the origin

On the derivatives of a polynomial with restricted zeros

ISSN	2197-120X, 2524-7581
h-index	5