Geometry and Topology of Manifolds : 10th China-Japan Conference 2014 / edited by Akito Futaki, Reiko Miyaoka, Zizhou Tang, Weiping Zhang.

Format:

Book

Conference/Event

Contributor:

Futaki, Akito., Editor.

Miyaoka, Reiko., Editor.

Tang, Zizhou., Editor.

Zhang, Weiping., Editor.

Conference Name:

Geometry Conference for the Friendship of China and Japan (10th : 2014 : Shanghai, China)

Series:

Springer Proceedings in Mathematics & Statistics, 2194-1017 ; 154

Language:

English

Subjects (All):

Geometry, Differential.

Manifolds (Mathematics).

Differential equations.

Differential Geometry.

Manifolds and Cell Complexes.

Differential Equations.

Local Subjects:

Differential Geometry.

Manifolds and Cell Complexes.

Differential Equations.

Physical Description:

1 online resource (350 p.)

Edition:

1st ed. 2016.

Place of Publication:

Tokyo : Springer Japan : Imprint: Springer, 2016.

Summary:

Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincaré conjecture, the Yau–Tian–Donaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among others, the Strominger–Yau–Zaslow conjecture on mirror symmetry, the relative Yau–Tian–Donaldson conjecture in Kähler geometry, the Hopf conjecture, and the Yau conjecture on the first eigenvalue of an embedded minimal hypersurface of the sphere. For the younger generation to approach such problems and obtain the required techniques, it is of the utmost importance to provide them with up-to-date information from leading specialists. The geometry conference for the friendship of China and Japan has achieved this purpose during the past 10 years. Their talks deal with problems at the highest level, often accompanied with solutions and ideas, which extend across various fields in Riemannian geometry, symplectic and contact geometry, and complex geometry.

Contents:

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 Theorem5 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 Variations3.1 Definition of λ-hypersurfaces; 3.2 mathcalF-Functional; 3.3 Stability of Compact λ-hypersurfaces; 3.4 Complete λ-hypersurfaces; 4 Area of Complete λ-hypersurfaces; 4.1 Upper Bound Growth of Area of Complete λ-hypersurfaces; 4.2 Lower Bound Growth of Area of Complete λ-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 Immersions4.1 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

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

4-431-56021-1