Contributions to Analysis. A Collection of Papers Dedicated to Lipman Bers

Contributors
Title page
Contents
List of Contributors
Preface
On the Decomposition and Deformation of Kleinian Groups - William Abikoff
	Introduction
	1. Some Kleinian Groups
	2. The Maskit Combination Theorems
	3. The Decomposition of Finitely Generated Kleinian Groups of the Second Kind
	4. Deformations of Finitely Generated Kleinian Groups
	References
Some Loci of Teichmiiller Space for Genus Five Defined by Vanishing - Theta Nulls, Robert D.M. Accola
	1. Introduction
	2. Riemann's Vanishing Theorem
	3. g31s on Surfaces of Genus Five
	4. Surfaces of Genus Five Admitting Two Half-Canonical #4's
	5. Proofs of the Theorems
	6. Necessary Conditions for Elliptic-Hyperellipticity
	7. Some Remarks on the p-2 Conjecture for Higher Genus
	References
Conditions for Quasiconformal Deformations in Several Variables - Lars V. Ahlfors
	1. Introduction
	2. Uniqueness
	3. The Adjoint Operator
	4. Statement of the Theorem
	5. Necessity
	6. Sufficiency
	References
On Locally Quasiconformal Mappings in Space (n > 3) - P.P. Belinskii and M.A. Lavrentiev
	References
A Theorem on the Boundary Correspondence under Conformal Mapping with Application to Free Boundary Problems of Fluid Dynamics - Paul W. Berg
	Introduction
	1. Boundary Correspondence Theorem
	2. Application to Cavity Flows
	References
The Extension Problem for Quasiconformal Mappings - Lennart Carleson
	References
Hyperbolic Spaces - S. S. Chen and L. Greenberg
	1. Introduction and Preliminaries
	2. The Hyperbolic Space H(f)
	3. Conjugacy Classes in i/(l,w;F)
	4. Subgroups of 1/(1,n;F)
	References
On ?-Monogenic Functions, and the Mean Value Theorem of the Differential Calculus - J.B. Diaz
	1. Reminiscence, and ?-Monogenic Functions
	2. Remarks on the Elementary Mean Value Theorem of the Differential Calculus
	Abstract (of Lecture)
	Lecture
	References
On Quasiconformal Extensions of the Beurling-Ahlfors Type - Clifford J. Earle
	1. Introduction
	2. Statement of Theorems
	3. Proof of Theorem 1
	4. Proof of Theorem 2
	5. Proof of Theorem 3
	References
On Holomorphic Mappings between Teichmiiller Spaces - Clifford J. Earle and Irwin Kra
	Introduction
	1. Teichmiiller Spaces
	2. The Teichmiiller Metric
	3. The Automorphism Group of T(gji)
	4. The Teichmiiller Curve and Its Sections
	5. Most Fiber Spaces Are Not Teichmiiller Spaces
	References
On the Poincare Relation - L. Ehrenpreis, H. M. Farkas, H. Martens, and  Rauch
	Introduction
	References
Elliptic Functions and Modular Forms - Farkas
	Introduction
	Reference
On the Differentiability of Solutions of Accretive Linear Differential Equations - К.О. Friedrichs
	References
Survey of Some Recent Progress in Transonic Aerodynamics - P.R. Garabedian
	1. Introduction
	2. Optimal Transonic Airfoils
	3. Three-Dimensional Problems
	References
The Hausdorff Measure of Sets Which Link in Euclidean Space - F.W. Gehring
	1. Introduction
	2. Preliminary Results
	3. Main Construction
	4. Main Results
	5. An Inequality for Quasiconformal Mappings
	References
Two Results in the Global Theory of Holomorphic Mappings - Phillip A. Griffiths
	Introduction
	1. Statement of Theorem I
	2. The First Main Theorem; A Result of Chern-Wu
	3. Two Estimates from the Theory of Holomorphic Curves
	4. Proof of Theorem I
	5. Some Comments and Examples
	6. Statement and Proof of Theorem II
	7. Some Comments and Questions regarding Holomorphic Curves
	References
On Fundamental Domains and the Teichmiiller Modular Group - Linda Keen
	1. Introduction
	2. The Torus with a Hole
	3. Geodesies on S
	4. The Twist Parameter
	References
Differential Equations in a Projective Space and Linear Dependence over a Projective Variety - E.R. Kolchin
	Introduction
	1. Canonical Characteristic Sets
	2. Differentially Homogeneous and Differentially Multihomogeneous Differential Polynomials
	3. Differentially Homogeneous and Differentially Multihomogeneous Differential Ideals
	4. Algebraic Differential Equations in Projective and Multiprojective Spaces
	5. Differential Specializations
	6. Differentially Complete Differentially Closed Sets
	7. Linear Dependence over Projective Varieties
	8. Examples
	References
On the Complexes on the Boundary Induced by Elliptic Complexes of Differential Operators - Masatake Kuranishi
	Introduction
	0. Preliminaries
	1. Normal Derivative Operators
	2. Operators Induced on the Boundary
	3. Operators on the Boundary Induced by the Elliptic Complex of Differential Operators
	References
Group Isomorphisms Induced by Quasiconformal Mappings - Olli Lehto
	References
Partial Differential Equations Invariant under Conformal or Projective Transformations - Charles Loewner and Louis Nirenberg
	Introduction
	Part I
	1. Derivation of Conditions (4) and (5) for Partial Conformal Invariant* of (3)
	2. The Dirichlet Problem for (6') in Domains with Smooth Compact Boundaries
	3. A Priori Estimates for Nonnegative Solutions of (2.1)
	4. Solutions of (6') Which Are Infinite on the Boundary
	5. Solutions of (6') for Arbitrary Domains in Rn
	Part II
	6. Invariance of (9) and (10) under Projective Transformations
	7. The Boundary Value Problem (9)
	8. A Priori Estimates for Second Derivatives
	9. The Metric (10) Is Complete
	10. The Mean Curvature of the Surface Is Bounded
	References
Schottky Groups and Circles - Albert Mar den
	1. Introduction
	2. Schottky Space
	3. Classical Schottky Space
	4. Convergence of Classical Schottky Groups
	5. Proof of the Proposition
	6. Proof of Theorem 3.1
	7. Fuchsian Groups of the Second Kind
	References
Homomorphisms Associated with Multiplicative Functions - Henrik H. Martens
	Introduction
	1. Complex Tori and Multiplicative Functions
	2. a(f,F)
	References
Uniformizations of Riemann Surfaces - Bernard Maskit
	Introduction
	1. What Is a Uniformization ?
	2. Isomorphisms
	3. Factor Subgroups
	4. Precisely Invariant Sets
	5. Picture of a Uniformization
	6. Standard Uniformizations
	7. Torsion-Free Uniformizations
	8. The General Uniformization Theorem
	References
Some Restrictions on the Smooth Immersion of Complete Surfaces in E3 - Tula Klotz Milnor
	Introduction
	1. Definitions
	2. Preliminary Results
	3. Some Theorems
	4. Subsidiary Results
	References
Prym Varieties I - David Mumford -
	Introduction
	Notations
	Part I
	1. Double Coverings of Curves
	2. A Configuration of Abelian Varieties
	3. Definition of the Prym Variety
	Part II
	4. Relations between Theta Divisors
	5. The Splitting of ?~?(??,!) for Jacobians
	Part III
	6. Geometric Description of Sing ?, Unramified Case
	7. Dim Sing ?
	Appendix: A Theorem of Martens
	References
Asymptotic Decay for Ultrahyperbolic Operators - Ptotter
	1. Introduction
	2. The Ultrahyperbolic Operator
	3. Generalized Ultrahyperbolic Operators
	References
Instability of Thin-Walled Spherical Structures under External Pressure - Harry E. Rauch
	1. Introduction
	2. Basic Equations
	3. Method of Solution of the Equations
	4. A Numerical Example
	5. Legendre Functions and the Coefficients (l,m,n)
	References
Extremal Quasiconformal Mappings with Given Boundary Values - Edgar Reich and Kurt Strebel
	Introduction
	1. Quasiconformal Mappings of the Unit Disc with the Same Boundary Values
	2. The Sufficiency of Hamilton's Condition
	3. Proof of Hamilton's Theorem (Necessity for Extremality)
	4. Some Consequences of Hamilton's Condition
	References
Invariant Metrics on Teichmuller Space - H.L. Royden
	1. Differential Metrics on Teichmuller Space
	2. Hermitian Metrics on T,
	3. Metrics Associated with the Embedding of T, in the Siegel Upper Half-Plane
	References
A Constructive Proof of the Riemann-Roch Theorem for Curves - L.M. Sibner and R.J. Sibner
	References
Function Theory on Diiferentiable Submanifolds - R.O. Wells, Jr.
	1. Introduction
	2. Holomorphic Approximation and Extension: Examples
	3. Holomorphic Approximation
	4. Envelopes of Holomorphy and Holomorphic Extension
	5. CR Function Theory
	References