Quasiconformal Extensions and Reflections

Krushkal, Samuel L.

doi:10.1016/s1874-5709(05)80015-0

Cited by 32 publications

(7 citation statements)

References 121 publications

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“…The Teichmüller and Grunsky norms are intrinsically connected with quasiconformal reflections, Fredholm eigenvalues and other quasiinvariants of quasiconformal curves. We outline briefly the main notions; the details see, e.g., in [1,[14][15][16].…”

Section: Fredholm Eigenvalues and Quasireflectionsmentioning

confidence: 99%

On the Extremality of Harmonic Beltrami Coefficients

Krushkal

2022

Mathematics

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We prove a general theorem, which provides a broad collection of univalent functions with equal Grunsky and Teichmüller norms and thereby the Fredholm eigenvalues and the reflection coefficients of associated quasicircles. It concerns an important problem to establish the exact or approximate values of basic quasiinvariant functionals of Jordan curves, which is crucial in applications and in the numerical aspect of quasiconformal analysis.

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Section: Fredholm Eigenvalues and Quasireflectionsmentioning

confidence: 99%

On the Extremality of Harmonic Beltrami Coefficients

Krushkal

2022

Mathematics

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“…In particular, using somewhat modification of Teichmüller's Verschiebungssatz [103], he established in [102] the reflection coefficient of the set E , which consists of the interval À2i,2i ½ and a separate point t > 0. All these results are presented in [64]. Theorems 4 and 6 open a new way in solving this problem following the lines of the first example after Theorem 4.…”

Section: Reflections Across Finite Collections Of Quasiintervals 61 mentioning

confidence: 79%

“…Holomorphic motions have been important in the study of dynamical systems, Kleinian groups, holomorphic families of conformal maps and of Riemann surfaces as well as in many other fields (see, e.g., [40,57,59,60,[62][63][64][65][66][67][68], and the references there).…”

Section: Holomorphic Motionsmentioning

confidence: 99%

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Quasiconformal Reflections across Polygonal Lines

Krushkal¹

2021

Structure Topology and Symplectic Geometry

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An important open problem in geometric complex analysis is to establish algorithms for explicit determination of the basic curvelinear and analytic functionals intrinsically connected with conformal and quasiconformal maps, such as their Teichmüller and Grunsky norms, Fredholm eigenvalues and the quasireflection coefficient. This has not been solved even for convex polygons. This case has intrinsic interest in view of the connection of polygons with the geometry of the universal Teichmüller space and approximation theory. This survey extends our previous survey of 2005 and presents the new approaches and recent essential progress in this field of geometric complex analysis, having various important applications. Another new topic concerns quasireflections across finite collections of quasiintervals.

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“…This bound cannot be improved in the general case. Holomorphic motions have been important in the study of dynamical systems, Kleinian groups, holomorphic families of conformal maps and of Riemann surfaces as well as in many other fields (see, e.g., [40,57,59,60,[62][63][64][65][66][67][68], and the references there).…”

Section: Holomorphic Motionsmentioning

confidence: 99%

Structure Topology and Symplectic Geometry

Shah¹,

Lei²

2021

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He obtained an MSc from Government Post Graduate Jehanzeb College Swat in 2005. He joined the University of Malakand as a lecturer in 2007. Dr. Shah obtained a Ph.D. in Fractional Calculus in 2016 from the University of Malakand. He has published numerous articles in scientific journals and has supervised many MPhil and Ph.D. students. Dr. Min Lei has worked at Shanghai Jiaotong University as an associate professor since 2004.

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Quasiconformal Extensions and Reflections

Cited by 32 publications

References 121 publications

On the Extremality of Harmonic Beltrami Coefficients

On the Extremality of Harmonic Beltrami Coefficients

Quasiconformal Reflections across Polygonal Lines

Structure Topology and Symplectic Geometry

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