Contributions to Analysis

A Collection of Papers Dedicated to Lipman Bers

Lars V. Ahlfors, Irwin Kra, Bernard Maskit

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780120448500
• eBook ISBN:
  9781483261164
• Topic: Mathematics
• Subtopic: Calculus
• Index: Mathematics

Contributions to Analysis: A Collection of Papers Dedicated to Lipman Bers is a compendium of papers provided by Bers, friends, students, colleagues, and professors. These papers deal with Teichmuller spaces, Kleinian groups, theta functions, algebraic geometry. Other papers discuss quasiconformal mappings, function theory, differential equations, and differential topology. One paper discusses the results of the rigidity theorem of Mostow and its generalization by Marden in relation to geometric properties of Kleinian groups of the first kind. These results, obtained by planar methods, are presented in terms of the hyperbolic 3-space language, which is a natural pedestal in approaching the action of the Kleinian groups. Another paper reviews Riemann's vanishing theorem which solves the Jacobi inversion problem, by relating the vanishing properties of the theta function (particularly at half periods) to properties of certain linear series on the Riemann surface. One paper examines the problem of obtaining relations among the periods of the differentials of first kind on a compact Riemann surface. An application of a computer program involves supersonic transport. The program is based on the hodograph transformation and a method of complex characteristics to calculate profiles that are shock-less at a specified angle of attack, or at a specified subsonic free-stream Mach number. The collection can prove useful for engineers, statisticians, students, and professors in advance mathematics or courses related to aeronautics.

Table of contents

• Front Cover
• Contributions to Analysis: A Collection of Papers Dedicated to Lipman Bers
• Copyright Page
• Table of Contents
• Contributors
• List of Contributors
• PREFACE
• Chapter 1. On the Decomposition and Deformation of Kleinian Groups
• Chapter 2. Some Loci of Teichműller Space for Genus Five Defined by Vanishing Theta Nulls
• Chapter 3. Conditions for Quasiconformal Deformations in Several Variables
• Chapter 4. On Locally Quasiconformal Mappings in Space (n ≥ 3)
• Chapter 5. A Theorem on the Boundary Correspondence under Conformal Mapping with Application to Free Boundary Problems of Fluid Dynamics
• Chapter 6. The Extension Problem for Quasiconformal Mappings
• Chapter 7. Hyperbolic Spaces
• Chapter 8. On ∑-Monogenic Functions, and the Mean Value Theorem of the Differential Calculus
• Chapter 9. On Quasiconformal Extensions of the Beurling-Ahlfors Type
• Chapter 10. On Holomorphic Mappings between Teichmüller Spaces
• Chapter 11. On the Poincare Relation
• Chapter 12. Elliptic Functions and Modular Forms
• Chapter 13. On the Differentiability of Solutions of Accretive Linear Differential Equations
• Chapter 14. Survey of Some Recent Progress in Transonic Aerodynamics
• Chapter 15. The Hausdorff Measure of Sets Which Link in Euclidean Space
• Chapter 16. Two Results in the Global Theory of Holomorphic Mappings
• Chapter 17. On Fundamental Domains and the Teichmüller Modular Group
• Chapter 18. Differential Equations in a Projective Space and Linear Dependence over a Projective Variety
• Chapter 19. On the Complexes on the Boundary Induced by Elliptic Complexes of Differential Operators
• Chapter 20. Group Isomorphisms Induced by Quasiconformal Mappings
• Chapter 21. Partial Differential Equations Invariant under Conformai or Projective Transformations
• Chapter 22. Schottky Groups and Circles
• Chapter 23. Homomorphisms Associated with Multiplicative Functions
• Chapter 24. Uniformizations of Riemann Surfaces
• Chapter 25. Some Restrictions on the Smooth Immersion of Complete Surfaces in E3
• Chapter 26. Prym Varieties I
• Chapter 27. Asymptotic Decay for Ultrahyperbolic Operators
• Chapter 28. Instability of Thin-Walled Spherical Structures under External Pressure
• Chapter 29. Extremal Quasiconformal Mappings with Given Boundary Values
• Chapter 30. Invariant Metrics on Teichmüller Space
• Chapter 31. A Constructive Proof of the Riemann-Roch Theorem for Curves
• Chapter 32. Function Theory on Differentiable Submanifolds