The Journal of Geometric Analysis, ISSN 1050-6926, 4/2017, Volume 27, Issue 2, pp. 1468 - 1488

The main aim of this article is to establish certain relationships between K-quasiconformal harmonic mappings and John disks...

Primary 30C65 | 30C75 | 30C45 | Secondary 30C20 | Mathematics | John disk | 30H10 | Abstract Harmonic Analysis | Pommerenke interior domain | Fourier Analysis | K -quasiconformal harmonic mappings | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Pre-Schwarzian derivative | Differential Geometry | Dynamical Systems and Ergodic Theory | K-quasiconformal harmonic mappings | CRITERIA | MATHEMATICS | PRE-SCHWARZIAN | DOMAINS

Primary 30C65 | 30C75 | 30C45 | Secondary 30C20 | Mathematics | John disk | 30H10 | Abstract Harmonic Analysis | Pommerenke interior domain | Fourier Analysis | K -quasiconformal harmonic mappings | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Pre-Schwarzian derivative | Differential Geometry | Dynamical Systems and Ergodic Theory | K-quasiconformal harmonic mappings | CRITERIA | MATHEMATICS | PRE-SCHWARZIAN | DOMAINS

Journal Article

TheScientificWorld, ISSN 2356-6140, 4/2014, Volume 2014, pp. 930571 - 9

We show that 1-quasiconformal mappings on Goursat groups are CR or anti-CR mappings...

QUASI-CONFORMAL MAPPINGS | HEISENBERG-GROUP | CONTACT | MAPS | CARNOT GROUPS | MULTIDISCIPLINARY SCIENCES | Quasiconformal mappings | Functions of complex variables | Research | Mathematical research | Group theory | Studies | Lie groups

QUASI-CONFORMAL MAPPINGS | HEISENBERG-GROUP | CONTACT | MAPS | CARNOT GROUPS | MULTIDISCIPLINARY SCIENCES | Quasiconformal mappings | Functions of complex variables | Research | Mathematical research | Group theory | Studies | Lie groups

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2017, Volume 446, Issue 2, pp. 1154 - 1166

We estimate the Jacobian of harmonic mapping of the unit disk onto a smooth and convex Jordan domain via the boundary function and the boundary curvature of the image domain...

Harmonic | Curvature | Quasiconformal | MATHEMATICS | MATHEMATICS, APPLIED | THEOREM | INEQUALITY | JORDAN DOMAINS

Harmonic | Curvature | Quasiconformal | MATHEMATICS | MATHEMATICS, APPLIED | THEOREM | INEQUALITY | JORDAN DOMAINS

Journal Article

Potential analysis, ISSN 1572-929X, 2018, Volume 50, Issue 3, pp. 415 - 437

In this article, we continue our investigations of the boundary behavior of harmonic mappings...

Geometry | Primary: 30C65, 30C75 | Pommerenke interior domain | Potential Theory | Functional Analysis | Secondary: 30C20, 30C45, 30H10 | K -quasiconformal harmonic mapping | Radial length | Probability Theory and Stochastic Processes | Mathematics | Radial John disk | K-quasiconformal harmonic mapping | MATHEMATICS

Geometry | Primary: 30C65, 30C75 | Pommerenke interior domain | Potential Theory | Functional Analysis | Secondary: 30C20, 30C45, 30H10 | K -quasiconformal harmonic mapping | Radial length | Probability Theory and Stochastic Processes | Mathematics | Radial John disk | K-quasiconformal harmonic mapping | MATHEMATICS

Journal Article

Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, 2018, Volume 43, pp. 981 - 990

We present a new and simple proof of Teichmfiller-Wittich-Belinskit's and Gutlyanskii-Martio's theorems on the conformality of quasiconformal mappings at a given point...

Quasiconformal mapping | MATHEMATICS | BEHAVIOR

Quasiconformal mapping | MATHEMATICS | BEHAVIOR

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 2019, Volume 42, Issue 5, pp. 2151 - 2168

The present article concerns the Bohr radius for K-quasiconformal sense-preserving harmonic mappings $$f=h+\overline{g}$$ f = h + g ¯ in the unit disk $$\mathbb {D...

Starlike and convex functions | Subordination | 30C45 | Primary 30A10 | Harmonic mappings | 30C62 | Mathematics, general | Secondary 30C75 | Mathematics | Applications of Mathematics | Bohr radius | K -quasiconformal mappings | MATHEMATICS | K-quasiconformal mappings

Starlike and convex functions | Subordination | 30C45 | Primary 30A10 | Harmonic mappings | 30C62 | Mathematics, general | Secondary 30C75 | Mathematics | Applications of Mathematics | Bohr radius | K -quasiconformal mappings | MATHEMATICS | K-quasiconformal mappings

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 9/2010, Volume 44, Issue 2, pp. 330 - 428

...Discrete Comput Geom (2010) 44: 330–428 DOI 10.1007/s00454-010-9269-9 Conformal Mapping in Linear Time Christopher J. Bishop Received: 29 April 2008 / Revised...

Computational Mathematics and Numerical Analysis | Convex hulls | Quasiconformal mappings | CRDT algorithm | Schwarz–Christoffel formula | Quasisymmetric mappings | Mathematics | Numerical conformal mappings | Hyperbolic 3-manifolds | Medial axis | Combinatorics | Sullivan’s theorem | Schwarz-Christoffel formula | Sullivan's theorem | TRANSFORMATION | VORONOI DIAGRAM | SIMPLE POLYGON | FAST ALGORITHM | MATHEMATICS | CIRCLE PACKINGS | SHAPE | MAPS | CONVERGENCE | BOUNDARY | COMPUTER SCIENCE, THEORY & METHODS | Computational geometry | Disks | Construction | Conformal mapping

Computational Mathematics and Numerical Analysis | Convex hulls | Quasiconformal mappings | CRDT algorithm | Schwarz–Christoffel formula | Quasisymmetric mappings | Mathematics | Numerical conformal mappings | Hyperbolic 3-manifolds | Medial axis | Combinatorics | Sullivan’s theorem | Schwarz-Christoffel formula | Sullivan's theorem | TRANSFORMATION | VORONOI DIAGRAM | SIMPLE POLYGON | FAST ALGORITHM | MATHEMATICS | CIRCLE PACKINGS | SHAPE | MAPS | CONVERGENCE | BOUNDARY | COMPUTER SCIENCE, THEORY & METHODS | Computational geometry | Disks | Construction | Conformal mapping

Journal Article

1966, Van Nostrand mathematical studies, 10, 146

Book

数学学报：英文版, ISSN 1439-8516, 2013, Volume 29, Issue 8, pp. 1543 - 1554

A homeomorphism w=f（z） of a domain D is called a locally quasiconformal mapping, if for each subdomain D＇ of D...

拟共形映照 | 拟共形映射 | 同胚 | 单位圆盘 | 30C75 | locally quasiconformal mapping | directional dilatation | Homeomorphism | 30C62 | Mathematics, general | Mathematics | quasiconformal mapping | MATHEMATICS | MATHEMATICS, APPLIED | BELTRAMI EQUATION | MU(Z)-HOMEOMORPHISMS | Studies | Mapping | Algebra | Constrictions | Discs | Disks | Dilatation | Mathematical analysis

拟共形映照 | 拟共形映射 | 同胚 | 单位圆盘 | 30C75 | locally quasiconformal mapping | directional dilatation | Homeomorphism | 30C62 | Mathematics, general | Mathematics | quasiconformal mapping | MATHEMATICS | MATHEMATICS, APPLIED | BELTRAMI EQUATION | MU(Z)-HOMEOMORPHISMS | Studies | Mapping | Algebra | Constrictions | Discs | Disks | Dilatation | Mathematical analysis

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 11/2005, Volume 91, Issue 3, pp. 655 - 702

The theory of mappings of finite distortion has arisen out of a need to extend the ideas and applications of the classical theory of quasiconformal mappings to the degenerate elliptic setting...

quasiconformal | calculus of variations | extremal | harmonic | MATHEMATICS | UNIVALENT HARMONIC-MAPPINGS | ANNULI | CONJECTURE

quasiconformal | calculus of variations | extremal | harmonic | MATHEMATICS | UNIVALENT HARMONIC-MAPPINGS | ANNULI | CONJECTURE

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 08/2011, Volume 363, Issue 8, pp. 4043 - 4061

Let \mathcal{QC}(K,g)-quasiconformal mappings of the open unit disk onto itself satisfying the PDE \Delta w =g g\in C(\overline{\mathbb{U}}). It is proved...

Harmonics | Mathematical theorems | Homeomorphism | Differentials | Mathematical functions | Mathematical inequalities | Partial derivatives | Spherical coordinates | Lipschitz condition | Quasiconformal harmonic maps | MATHEMATICS | BOUNDARY CORRESPONDENCE | BALL | MAPS | HARMONIC-MAPPINGS | DOMAINS | QUASICONFORMAL MAPPINGS

Harmonics | Mathematical theorems | Homeomorphism | Differentials | Mathematical functions | Mathematical inequalities | Partial derivatives | Spherical coordinates | Lipschitz condition | Quasiconformal harmonic maps | MATHEMATICS | BOUNDARY CORRESPONDENCE | BALL | MAPS | HARMONIC-MAPPINGS | DOMAINS | QUASICONFORMAL MAPPINGS

Journal Article

32.
Full Text
Thurston's metric on Teichmüller space and the translation distances of mapping classes

Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, 2016, Volume 41, Issue 2, pp. 867 - 879

... with boundary, equipped with their arc metrics, when the boundary lengths tend to zero. We use this to obtain a result on the translation distances of mapping classes...

Hyperbolic geometry | Translation distance | Pseudo-Anosov | Teichmüller space | Thurston metric | Quasiconformal mapping | Reducible | Arc metric | Mapping class group | MATHEMATICS | arc metric | mapping class group | Teichmuller space | hyperbolic geometry | translation distance | pseudo-Anosov | BOUNDARY | quasiconformal mapping | reducible | SURFACES | Geometric Topology | Mathematics

Hyperbolic geometry | Translation distance | Pseudo-Anosov | Teichmüller space | Thurston metric | Quasiconformal mapping | Reducible | Arc metric | Mapping class group | MATHEMATICS | arc metric | mapping class group | Teichmuller space | hyperbolic geometry | translation distance | pseudo-Anosov | BOUNDARY | quasiconformal mapping | reducible | SURFACES | Geometric Topology | Mathematics

Journal Article

33.
Full Text
Coefficients Estimate for Harmonic v-Bloch Mappings and Harmonic K-Quasiconformal Mappings

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 1/2016, Volume 39, Issue 1, pp. 349 - 358

Let $$f(z)=h(z)+\overline{g(z)}$$ f ( z ) = h ( z ) + g ( z ) ¯ be a harmonic v-Bloch mapping defined in the unit disk $${\mathbb {D}}$$ D with $$\Vert f\Vert...

Bloch constant | Primary 30C62 | Harmonic quasiconformal mappings | Harmonic v -Bloch mappings | 30F15 | Mathematics, general | Secondary 30C20 | Mathematics | Applications of Mathematics | Coefficient estimates | Harmonic v-Bloch mappings | MATHEMATICS | BOUNDARY CORRESPONDENCE | CONSTANT | Theorems | Mapping

Bloch constant | Primary 30C62 | Harmonic quasiconformal mappings | Harmonic v -Bloch mappings | 30F15 | Mathematics, general | Secondary 30C20 | Mathematics | Applications of Mathematics | Coefficient estimates | Harmonic v-Bloch mappings | MATHEMATICS | BOUNDARY CORRESPONDENCE | CONSTANT | Theorems | Mapping

Journal Article

2009, Princeton mathematical series, ISBN 0691137773, Volume 48, xvi, 677

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis...

Differential equations, Elliptic | Quasiconformal mappings | Mathematics

Differential equations, Elliptic | Quasiconformal mappings | Mathematics

Book

Nonlinear analysis, ISSN 0362-546X, 2015, Volume 115, pp. 62 - 70

In this paper, we give bounds for length and area distortion for harmonic K-quasiconformal mappings, and investigate certain Lipschitz-type spaces on harmonic...

Hardy and Lipschitz spaces | Quasiconformal mappings | Harmonic and Bloch mappings | Length | Area function | Hardy and lipschitz spaces | Harmonic and bloch mappings | MATHEMATICS, APPLIED | LANDAUS THEOREM | QUASI-CONFORMAL MAPPINGS | CONSTANT | EQUIVALENT NORMS | BLOCH | MATHEMATICS | HOLOMORPHIC-FUNCTIONS | Harmonics | Distortion | Nonlinearity | Mapping

Hardy and Lipschitz spaces | Quasiconformal mappings | Harmonic and Bloch mappings | Length | Area function | Hardy and lipschitz spaces | Harmonic and bloch mappings | MATHEMATICS, APPLIED | LANDAUS THEOREM | QUASI-CONFORMAL MAPPINGS | CONSTANT | EQUIVALENT NORMS | BLOCH | MATHEMATICS | HOLOMORPHIC-FUNCTIONS | Harmonics | Distortion | Nonlinearity | Mapping

Journal Article

36.
Full Text
MAPPING PROPERTIES OF A SCALE INVARIANT CASSINIAN METRIC AND A GROMOV HYPERBOLIC METRIC

Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 02/2018, Volume 97, Issue 1, pp. 141 - 152

We consider a scale invariant Cassinian metric and a Gromov hyperbolic metric. We discuss a distortion property of the scale invariant Cassinian metric under...

hyperbolic-type metrics | the scale invariant Cassinian metric | quasiconformal map | uniform continuity | Möbius map | the Gromov hyperbolic metric | MATHEMATICS | Mobius map

hyperbolic-type metrics | the scale invariant Cassinian metric | quasiconformal map | uniform continuity | Möbius map | the Gromov hyperbolic metric | MATHEMATICS | Mobius map

Journal Article

Czechoslovak Mathematical Journal, ISSN 0011-4642, 3/2019, Volume 69, Issue 1, pp. 183 - 195

In this paper, we estimate the Douglas-Dirichlet functionals of harmonic mappings, namely Euclidean harmonic mapping and flat harmonic mapping, by using the extremal dilatation of finite distortion...

30C62 | Mathematics | Douglas-Dirichlet functional | extremal quasiconformal mapping | 31A05 | Ordinary Differential Equations | ϱ -harmonic mapping | Analysis | Convex and Discrete Geometry | Dirichlet’s principle | Mathematics, general | 30C70 | Mathematical Modeling and Industrial Mathematics | finite distortion functions | ϱ-harmonic mapping | MATHEMATICS | Dirichlet's principle | rho-harmonic mapping | HARMONIC MAPS | EXTREMAL MAPPINGS | UNIQUENESS | Computer science

30C62 | Mathematics | Douglas-Dirichlet functional | extremal quasiconformal mapping | 31A05 | Ordinary Differential Equations | ϱ -harmonic mapping | Analysis | Convex and Discrete Geometry | Dirichlet’s principle | Mathematics, general | 30C70 | Mathematical Modeling and Industrial Mathematics | finite distortion functions | ϱ-harmonic mapping | MATHEMATICS | Dirichlet's principle | rho-harmonic mapping | HARMONIC MAPS | EXTREMAL MAPPINGS | UNIQUENESS | Computer science

Journal Article

Filomat, ISSN 0354-5180, 2018, Volume 32, Issue 15, pp. 5371 - 5383

A sufficient condition of a flat harmonic quasiconformal mapping to be a quasihyperbolic quasiisometry on any subdomain of C is given in this paper, which generalizes the corresponding results...

Schwarz lemma | Quasiregular mapping | ϕ-Harmonic quasiconformal mapping | Quasihyperbolic quasi-isometry | Euclidean harmonic mapping | MATHEMATICS | MATHEMATICS, APPLIED | MAPS | UNIFORM DOMAINS | CURVATURE | CONFORMAL MAPPINGS | CONSTANT | phi-Harmonic quasiconformal mapping

Schwarz lemma | Quasiregular mapping | ϕ-Harmonic quasiconformal mapping | Quasihyperbolic quasi-isometry | Euclidean harmonic mapping | MATHEMATICS | MATHEMATICS, APPLIED | MAPS | UNIFORM DOMAINS | CURVATURE | CONFORMAL MAPPINGS | CONSTANT | phi-Harmonic quasiconformal mapping

Journal Article

Measurement, ISSN 0263-2241, 02/2016, Volume 80, pp. 270 - 280

.... Kernel trick improves largely the performance of learning system including recognition, clustering, prediction through the nonlinear kernel mapping from the input data space to output data space...

Quasiconformal multi-kernels learning | Kernel learning | Machine learning | Hyperspectral image classification | INSTRUMENTS & INSTRUMENTATION | ENGINEERING, MULTIDISCIPLINARY | CLASSIFICATION | Remote sensing | Electrical engineering | Visual learning

Quasiconformal multi-kernels learning | Kernel learning | Machine learning | Hyperspectral image classification | INSTRUMENTS & INSTRUMENTATION | ENGINEERING, MULTIDISCIPLINARY | CLASSIFICATION | Remote sensing | Electrical engineering | Visual learning

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2011, Volume 251, Issue 2, pp. 361 - 374

For a subgroup of the quasiconformal mapping class group of a Riemann surface in general, we give an algebraic condition which guarantees its discreteness in the compact-open topology...

Teichmüller space | Polycyclic | Discrete | Quasiconformal mapping class group | discrete | MATHEMATICS | polycyclic | Teichmuller space | DIMENSIONAL TEICHMULLER-SPACES | quasiconformal mapping class group

Teichmüller space | Polycyclic | Discrete | Quasiconformal mapping class group | discrete | MATHEMATICS | polycyclic | Teichmuller space | DIMENSIONAL TEICHMULLER-SPACES | quasiconformal mapping class group

Journal Article

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