Quasiregular Mappings

Quasiregular Mappings

by Seppo Rickman

Paperback(Softcover reprint of the original 1st ed. 1993)

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Product Details

ISBN-13: 9783642782039
Publisher: Springer Berlin Heidelberg
Publication date: 12/30/2011
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics , #26
Edition description: Softcover reprint of the original 1st ed. 1993
Pages: 213
Product dimensions: 6.69(w) x 9.53(h) x 0.02(d)

Table of Contents

I. Basic Properties of Quasiregular Mappings.- 1. ACLp Mappings.- 2. Quasiregular Mappings.- 3. Examples.- 4. Discrete Open Mappings.- II. Inequalities for Moduli of Path Families.- 1. Modulus of a Path Family.- 2. The KO-Inequality.- 3. Path Lifting.- 4. Linear Dilatations.- 5. Poletski?’s Lemma.- 6. Characterizations of Quasiregularity.- 7. Proof of Poletski?’s Lemma.- 8. Poletski?’s Inequality.- 9. Väisälä’s Inequality.- 10. Capacity Inequalities.- III. Applications of Modulus Inequalities.- 1. Global Distortion.- 2. Sets of Capacity Zero and Singularities.- 3. The Injectivity Radius of a Local Homeomorphism.- 4. Local Distortion.- 5. Bounds for the Local Index.- IV. Mappings into the n-Sphere with Punctures.- 1. Coverings Averages.- 2. The Analogue of Picard’s Theorem.- 3. Mappings of a Ball.- V. Value Distribution.- 1. Defect Relation.- 2. Coverings and Decomposition of Balls.- 3. Estimates on Liftings.- 4. Extremal Maximal Sequences of Liftings.- 5. Effect of the Defect Sum on the Liftings.- 6. Completion of the Proof of Defect Relations.- 7. Mappings of the Plane.- 8. Order of Growth.- 9. Further Results.- VI. Variational Integrals and Quasiregular Mappings.- 1. Extremals of Variational Integrals.- 2. Extremals and Quasiregular Mappings.- 3. Growth Estimates for Extremals.- 4. Differentiability of Quasiregular Mappings.- 5. Discreteness and Openness of Quasiregular Mappings.- 6. Pullbacks of General Kernels.- 7. Further Properties of Extremals.- 8. The Limit Theorem.- VII. Boundary Behavior.- 1. Removability.- 2. Asymptotic and Radial Limits.- 3. Continuity Results and the Reflection Principle.- 4. The Wiener Condition.- 5. F-Harmonic Measure.- 6. Phragmén-Lindelöf Type Theorems.- 7. Asymptotic Values.- List of Symbols.

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