Author | Rickman, Seppo. author |
---|---|
Title | Quasiregular Mappings [electronic resource] / by Seppo Rickman |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1993 |
Connect to | http://dx.doi.org/10.1007/978-3-642-78201-5 |
Descript | X, 213 p. online resource |
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?โs Lemma -- 6. Characterizations of Quasiregularity -- 7. Proof of Poletski?โs Lemma -- 8. Poletski?โs Inequality -- 9. Vรคisรคlรคโs 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 Picardโs 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. Phragmรฉn-Lindelรถf Type Theorems -- 7. Asymptotic Values -- List of Symbols