Invariant Distances and Metrics in Complex Analysis 2nd Edition by Marek Jarnicki, Peter Pflug ISBN 3110253860 9783110253863

Invariant Distances and Metrics in Complex Analysis 2nd Edition by Marek Jarnicki, Peter Pflug – Ebook PDF Instant Download/Delivery: 3110253860, 9783110253863
Full download Invariant Distances and Metrics in Complex Analysis 2nd Edition after payment

Product details:

ISBN 10: 3110253860
ISBN 13: 9783110253863
Author: Marek Jarnicki, Peter Pflug

Invariant Distances and Metrics in Complex Analysis 2nd Table of contents:

1 Hyperbolic geometry of the unit disc
1.1 Hyperbolic geometry of the unit disc
1.2 Some applications
1.3 Exercises
1.4 List of problems
2 The Carathéodory pseudodistance and the Carathéodory-Reiffen pseudometric
2.1 Definitions. General Schwarz-Pick lemma
2.2 Balanced domains
2.2.1 Operator h ↦ У
2.2.2 Operator h ↦ h̃
2.2.3 Operator h ↦ Wh
2.2.4 d-balanced domains
2.3 Carathéodory pseudodistance and pseudometric in balanced domains
2.4 Carathéodory isometries
2.5 Carathéodory hyperbolicity
2.6 The Carathéodory topology
2.7 Properties of c(*) and γ. Length of curve. Inner Carathéodory pseudodistance
2.8 ci -hyperbolicity versus c-hyperbolicity
2.9 Two applications
2.10 A class of n-circled domains
2.11 Neile parabola
2.12 Exercises
2.13 List of problems
3 The Kobayashi pseudodistance and the Kobayashi-Royden pseudometric
3.1 The Lempert function and the Kobayashi pseudodistance
3.2 Tautness
3.3 General properties of k
3.4 An extension theorem
3.5 The Kobayashi-Royden pseudometric
3.6 The Kobayashi-Buseman pseudometric
3.7 Product formula
3.8 Higher-order Lempert functions and Kobayashi-Royden pseudometrics
3.9 Exercises
3.10 List of problems
4 Contractible systems
4.1 Abstract point of view
4.2 Extremal problems for plurisubharmonic functions
4.2.1 Properties of gG and AG
4.2.2 Examples
4.2.3 Properties of SG
4.2.4 Properties of m(k)G and γ(K)G
4.3 Inner pseudodistances. Integrated forms. Derivatives. Buseman pseudometrics. C1-pseudodistances
4.3.1 Operator d ↦ di
4.3.2 Operator δ ↦ ∫δ
4.3.3 Operator δ ↦ Dδ
4.3.4 Operator δ ↦ δ̂
4.3.5 Operator δ ↦δ̃
4.3.6 C1-pseudodistances
4.4 Exercises
4.5 List of problems
5 Properties of standard contractible systems
5.1 Regularity properties of gG and AG
5.2 Lipschitz continuity of ℓ*, ϰ, g, and A
5.3 Derivatives
5.4 List of problems
6 Elementary Reinhardt domains
6.1 Elementary n-circled domains
6.2 General point of view
6.3 Elementary n-circled domains II
6.4 Exercises
6.5 List of problems
7 Symmetrized polydisc
7.1 Symmetrized bidisc
7.2 Symmetrized polydisc
7.3 List of problems
8 Non-standard contractible systems
8.1 Hahn function and pseudometric
8.2 Generalized Green, Möbius, and Lempert functions
8.3 Wu pseudometric
8.4 Exercises
8.5 List of problems
9 Contractible functions and metrics for the annulus
9.1 Contractible functions and metrics for the annulus
9.2 Exercises
9.3 List of problems
10 Elementary n-circled domains III
10.1 Elementary n-circled domains III
10.2 List of problems
11 Complex geodesics. Lempert’s theorem
11.1 Complex geodesics
11.2 Lempert’s theorem
11.3 Uniqueness of complex geodesics
11.4 Poletsky-Edigarian theorem
11.4.1 Proof of Theorem 11.4.5
11.5 Schwarz lemma – the case of equality
11.6 Criteria for biholomorphicity
11.7 Exercises
11.8 List of problems
12 The Bergman metric
12.1 The Bergman kernel
12.2 Minimal ball
12.3 The Lu Qi-Keng problem
12.4 Bergman exhaustiveness
12.5 Bergman exhaustiveness II – plane domains
12.6 L2h-domains of holomorphy
12.7 The Bergman pseudometric
12.8 Comparison and localization
12.9 The Skwarczynski pseudometric
12.10 Exercises
12.11 List of problems
13 Hyperbolicity
13.1 Global hyperbolicity
13.2 Local hyperbolicity
13.3 Hyperbolicity for Reinhardt domains
13.4 Hyperbolicities for balanced domains
13.5 Hyperbolicities for Hartogs type domains
13.6 Hyperbolicities for tube domains
13.7 Exercises
13.8 List of problems
14 Completeness
14.1 Completeness – general discussion
14.2 Carathéodory completeness
14.3 c-completeness for Reinhardt domains
14.4 ∫ γ(k)-completeness for Zalcman domains
14.5 Kobayashi completeness
14.6 Exercises
14.7 List of problems
15 Bergman completeness
15.1 Bergman completeness
15.2 Reinhardt domains and b-completeness
15.3 List of problems
16 Complex geodesics – effective examples
16.1 Complex geodesics in the classical unit balls
16.2 Geodesics in convex complex ellipsoids
16.3 Extremal discs in arbitrary complex ellipsoids
16.4 Biholomorphisms of complex ellipsoids
16.5 Complex geodesics in the minimal ball
16.6 Effective formula for the Kobayashi-Royden metric in certain complex ellipsoids
16.6.1 Formula for ϰℰ((1,m))
16.6.2 Formula for ϰℰ((1/2, 1/2))
16.7 Complex geodesics in the symmetrized bidisc
16.8 Complex geodesics in the tetrablock
16.9 Exercises
16.10 List of problems
17 Analytic discs method
17.1 Relative extremal function
17.2 Disc functionals
17.3 Poisson functional
17.4 Green, Lelong, and Lempert functionals
17.5 Exercises
18 Product property
18.1 Product property – general theory
18.2 Product property for the Möbius functions
18.3 Product property for the generalized Möbius function
18.4 Product property for the Green function
18.5 Product property for the relative extremal function
18.6 Product property for the generalized Green function
18.7 Product property for the generalized Lempert function
18.8 Exercises
18.9 List of problems
19 Comparison on pseudoconvex domains
19.1 Strongly pseudoconvex domains
19.2 The boundary behavior of the Carathéodory and the Kobayashi distances
19.3 Localization
19.4 Boundary behavior of the Carathéodory-Reiffen and the Kobayashi-Royden metrics
19.5 A comparison of distances
19.6 Characterization of the unit ball by its automorphism group
19.7 Exercises
19.8 List of problems
20 Boundary behavior of invariant functions and metrics on general domains
20.1 Boundary behavior of pseudometrics for non pseudoconvex domains
20.2 Boundary behavior of ϰ on pseudoconvex domains in normal direction
20.3 An upper boundary estimate for the Lempert function
20.4 Exercises
20.5 List of problems
A Miscellanea
A.1 Carathéodory balls
A.2 The automorphism group of bounded domains
A.3 Symmetrized ellipsoids
A.4 Holomorphic curvature
A.5 Complex geodesics
A.6 Criteria for biholomorphicity
A.7 Isometries
A.8 Boundary behavior of contractible metrics on weakly pseudoconvex domains
A.9 Spectral ball
A.10 List of problems
B Addendum
B.1 Holomorphic functions
B.1.1 Analytic sets
B.2 Proper holomorphic mappings
B.3 Automorphisms
B.3.1 Automorphisms of the unit disc
B.3.2 Automorphisms of the unit polydisc
B.3.3 Automorphisms of the unit Euclidean ball
B.4 Subharmonic and plurisubharmonic functions
B.5 Green function and Dirichlet problem
B.6 Monge-Ampère operator
B.7 Domains of holomorphy and pseudoconvex domains
B.7.1 Stein manifolds
B.8 L2-holomorphic functions
B.9 Hardy spaces
B.10 Kronecker theorem
B.11 List of problems
C List of problems

People also search for Invariant Distances and Metrics in Complex Analysis 2nd:

    
what is metrics analysis
    
complexity invariant distance
    
invariant measure logistic map
    
invariant coordinate selection
    
invariant distance

Tags: Marek Jarnicki, Peter Pflug, Distances, Metrics, Complex Analysis