On the evolution of harmonic mappings of Riemannian surfaces

Michael Struwe

doi:10.1007/bf02567432

On the evolution of harmonic mappings of Riemannian surfaces

Commentarii Mathematici Helvetici ◽

10.1007/bf02567432 ◽

1985 ◽

Vol 60 (1) ◽

pp. 558-581 ◽

Cited By ~ 232

Author(s):

Michael Struwe

Keyword(s):

Harmonic Mappings ◽

Riemannian Surfaces

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The Radó–Kneser–Choquet theorem for $p$-harmonic mappings between Riemannian surfaces

Revista Matemática Iberoamericana ◽

10.4171/rmi/1183 ◽

2020 ◽

Vol 36 (6) ◽

pp. 1779-1834

Author(s):

Tomasz Adamowicz ◽

Jarmo Jääskeläinen ◽

Aleksis Koski

Keyword(s):

Harmonic Mappings ◽

Riemannian Surfaces

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A Class of Harmonic Starlike Functions defined by Multiplier Transformation

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.1.36 ◽

2020 ◽

pp. 455-469

Author(s):

Deepali Khurana ◽

Raj Kumar ◽

Sibel Yalcin

Keyword(s):

Convex Combination ◽

Univalent Functions ◽

Extreme Points ◽

Starlike Functions ◽

Harmonic Mappings ◽

Distortion Bounds ◽

Radius Of Convexity ◽

Univalent Harmonic Mappings ◽

Harmonic Starlike ◽

Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

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On a Subclass of Univalent Harmonic Mappings Convex in the Imaginary Direction

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.1.35 ◽

2020 ◽

pp. 445-454

Author(s):

Deepali Khurana ◽

Sushma Gupta ◽

Sukhjit Singh

Keyword(s):

Present Article ◽

Unit Disk ◽

Imaginary Axis ◽

Harmonic Mappings ◽

Open Unit ◽

Open Unit Disk ◽

Distortion Bounds ◽

Univalent Harmonic Mappings

In the present article, we consider a class of univalent harmonic mappings, $\mathcal{C}_{T} = \left\{ T_{c}[f] =\frac{f+czf'}{1+c}+\overline{\frac{f-czf'}{1+c}}; \; c>0\;\right\}$ and $f$ is convex univalent in $\mathbb{D}$, whose functions map the open unit disk $\mathbb{D}$ onto a domain convex in the direction of the imaginary axis. We estimate coefficient, growth and distortion bounds for the functions of the same class.

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