Geometry and Topology of Manifolds

Name: Geometry and Topology of Manifolds | 10th China-Japan Conference 2014
Brand: Springer
Price: 96.29 EUR
Availability: OnlineOnly

10th China-Japan Conference 2014

Akito Futaki Reiko Miyaoka Zizhou Tang Weiping Zhang(Herausgeber*in)

Springer (Verlag)

Erschienen am 3. Juni 2016

XII, 348 Seiten

E-Book

PDF mit Wasserzeichen-DRM

Systemvoraussetzungen

978-4-431-56021-0 (ISBN)

96,29 €inkl. 7% MwSt.

Systemvoraussetzungen

für PDF mit Wasserzeichen-DRM

E-Book Einzellizenz

Als Download verfügbar

Beschreibung

Weitere Details

Weitere Ausgaben

Inhalt

Intro
Preface
Contents
Minimal Legendrian Surfaces in the Five-Dimensional Heisenberg Group
1 Introduction and Main Results
2 Some Known Results and Proof of Theorem1.1
3 Proof of Theorem1.4
References
Gluing Principle for Orbifold Stratified Spaces
1 Introduction and Statements of Main Theorems
2 Smooth Structures on Stratified Orbifolds
2.1 Linearly Stratified (Euclidean) Spaces
2.2 Gluing Principle for Manifold Stratified Spaces
2.3 Gluing Theorem for Orbifold Stratified Spaces
3 Moduli Spaces of Stable Curves as Orbifold Stratified Spaces
3.1 Teichmüller Space and Moduli Space of Riemann Surfaces (Top Stratum)
3.2 Canonical Construction of Proper'etale Groupoids
3.3 Moduli Space of Stable Curves
4 Horocycle Structures Associated to Marked or Nodal Points
5 Gluing Data and Good Orbifold Gluing Structures for Moduli Spaces of Stable Curves
References
Applications of the Affine Structures on the Teichmüller Spaces
1 Introduction
2 Period Maps on Moduli Spaces
2.1 Moduli, Torelli and Teichmüller space
2.2 Period Domain and Period Map
3 Affine Structures on Teichmüller Spaces
4 Hodge Metric Completion Space of Torelli Space and a Global Torelli Theorem
5 Applications
5.1 Surjectivity of the Period Map on the Hodge Metric Completion Space
5.2 Global Holomorphic Sections of the Hodge Bundles
5.3 A Global Splitting Property of the Hogde Bundles
References
Critical Points of the Weighted Area Functional
1 Introduction
1.1 Mean Curvature Flow
1.2 Mean Curvature Type Flow
2 Complete Self-shrinkers of Mean Curvature Flow
2.1 Definition of Self-shrinkers
2.2 Examples of Complete Self-shrinkers
2.3 Self-shrinkers with Non-negative Mean Curvature
3 The Weighted Volume-Preserving Variations
3.1 Definition of ?-hypersurfaces
3.2 mathcalF-Functional
3.3 Stability of Compact ?-hypersurfaces
3.4 Complete ?-hypersurfaces
4 Area of Complete ?-hypersurfaces
4.1 Upper Bound Growth of Area of Complete ?-hypersurfaces
4.2 Lower Bound Growth of Area of Complete ?-hypersurfaces
References
A New Look at Equivariant Minimal Lagrangian Surfaces in mathbbC P2
1 Introduction
2 Minimal Lagrangian Surfaces in mathbbCP2
2.1 The Loop Group Method for Minimal Lagrangian Surfaces
3 Equivariant Minimal Lagrangian Surfaces
4 Translationally Equivariant Minimal Lagrangian Immersions
4.1 Application of a Result by Burstall and Kilian for Translationally Equivariant Minimal Lagrangian Immersions
5 Explicit Iwasawa Decomposition for Translationally Equivariant Minimal Lagrangian Immersions
5.1 The Basic Set-Up
5.2 Evaluation of the Characteristic Polynomial Equations
5.3 Explicit Solutions for Metric and Cubic Form
5.4 Explicit Iwasawa Decompositions
5.5 Explicit Expressions for Minimal Lagrangian Immersions
6 Equivariant Cylinders and Tori
6.1 Translationally Equivariant Minimal Lagrangian Cylinders
6.2 Translationally Equivariant Minimal Lagrangian Tori
7 Comparison with the Work of Castro-Urbano
7.1 The Case of Non-invertible D(?)
7.2 The Case of Non-real ?-3?
7.3 The Case of Real ?-3?
References
A Survey on Balanced Metrics
1 Introduction
2 Existence Theorems of Balanced Metrics
3 Deformation Stability of Existence of Balanced metrics
4 Balanced Metrics on Non--Kähler Calabi--Yau Threefolds
5 Form-Type Calabi-Yau Equations
6 The Balanced Cone of a Kähler Manifold
References
Can One Hear the Shape of a Group?
1 Marked Length Spectrum
2 Coarsely Isometric Metrics and Conjecture by Margulis
3 Marked Length Iso-spectrum and (1,C)-Quasi-isometry
4 Heisenberg Groups
References
Differential Topology Interacts with Isoparametric Foliations
1 Introduction
2 Singular Riemannian Foliations and Isoparametric Foliations
3 Interaction Between 4-manifolds and SRF
4 Isoparametric Foliations on Homotopy Spheres
5 Application to Existence of Exotic Smooth Structures
References
Unobstructed Deformations of Generalized Complex Structures Induced by Cinfty Logarithmic Symplectic Structures and Logarithmic Poisson Structures
1 Introduction
2 Generalized Complex Structures
3 Deformation Theory of Generalized Complex Structures
4 Log Symplectic Structure ?mathbbC in Holomorphic Category and Generalized Complex Structure mathcalJf
5 Lie Algebroid Cohomology Groups of mathcalJf and Logarithmic Poisson Structure ß
6 Unobstructed Deformations of Generalized Complex Structures Induced from Cinfty Logarithmic Symplectic Structures
7 Logarithmic Deformations of mathcalJf
8 Proof of Main Theorems
9 Generalized Complex Structures on 4-manifolds
9.1 Non-degenerate, Pure Spinors of Even Type on 4-manifolds
9.2 Unobstructed Deformations of Generalized Complex Structures on Poisson Surfaces
9.3 Cinfty Logarithmic Transformations and Unobstructed Deformations of Generalized Complex Structures
References
The Symplectic Critical Surfaces in a Kähler Surface
1 Symplectic Surfaces
2 ß-symplectic Critical Surfaces
3 Examples in C2
4 Equations and Topological Properties
5 The Second Variation Formula
References
Some Evolution Problems in the Vacuum Einstein Equations
1 The Formation of Trapped Surface
2 The Local Extension of the Future Null Infinity
References
Willmore 2-Spheres in Sn: A Survey
1 Introduction
2 Möbius Invariant Surface Theory
3 Adjoint Transform: A Generalization of the Dual Willmore Surface
4 Global Aspect: Willmore 2-Spheres in S5
5 Loop Group Methods for Willmore Surfaces
5.1 The DPW Methods and Burstall-Guest's Classification of Harmonic Two-Spheres
5.2 Wilmore Surfaces in Terms of DPW
5.3 Coarse Classification of Willmore 2-Spheres
References
The Yau-Tian-Donaldson Conjecture for General Polarizations, I
1 Introduction
2 The Donaldson-Futaki Invariant F1 on mathcalM
3 Test Configurations Associated to Balanced Metrics
4 Proof of Main Theorem
References
Behavior of Gaussian Curvature and Mean Curvature Near Non-degenerate Singular Points on Wave Fronts
1 Introduction
2 Limiting Normal Curvature
3 Cuspidal Curvature
4 Singularities of the Second Kind
References
The Calabi Invariant and Central Extensions of Diffeomorphism Groups
1 Introduction
2 The Euler Class and Connection Cochains
3 Simplicial de Rham Model of Classifying Spaces
4 The Calabi Invariant
5 The Calabi Extension
6 Transgression Formula for the Calabi Invariant
References
Concentration, Convergence, and Dissipation of Spaces
1 Introduction
2 Observable Diameter and Separation Distance
3 Box Distance and Observable Distance
4 Pyramid
5 Dissipation
6 Limit Formula
7 Phase Transition Property
8 Critical Scale Limit of Spheres and Complex Projective Spaces
References
The Space of Left-Invariant Riemannian Metrics
1 Introduction
2 A Brief History
3 Preliminaries on Cohomogeneity One Actions
4 The Space of Left-Invariant Metrics
5 Milnor-Type Theorems
6 The Corresponding Submanifolds
References
Futaki Invariant and CM Polarization
1 Futaki Invariant and Its Residue Formula
2 Ding-Tian's Generalization
3 Donaldson's Generalization
4 CM Polarization
5 Asymptotics of K-Energy
References

Inhalt (PDF)

Systemvoraussetzungen

Als PDF speichern Als Link merken