GEOMETRY AND TOPOLOGY OF MANIFOLDS. 10TH CHINA-JAPAN CONFERENCE 2014

1. Minimal Legendrian Surfaces in the Five-Dimensional Heisenberg Group
2. Gluing Principle for Orbifold Stratified Spaces
3. Applications of the Affine Structures on the Teichmüller Spaces
4. Critical Points of the Weighted Area Functional
5. A New Look at Equivariant Minimal Lagrangian Surfaces in
6. A Survey on Balanced Metrics
7. Can One Hear the Shape of a Group?
8. Differential Topology Interacts with Isoparametric Foliations
9. Unobstructed Deformations of Generalized Complex Structures Induced by
10. The Symplectic Critical Surfaces in a Kähler Surface
11. Some Evolution Problems in the Vacuum Einstein Equations
12. Willmore 2-Spheres in
13. The Yau-Tian-Donaldson Conjecture for General Polarizations, I
14. Behavior of Gaussian Curvature and Mean Curvature Near Non-degenerate Singular Points on Wave Fronts
15. The Calabi Invariant and Central Extensions of Diffeomorphism Groups
16. Concentration, Convergence, and Dissipation of Spaces
17. The Space of Left-Invariant Riemannian Metrics
18. Futaki Invariant and CM Polarization

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.

Features
• Shows recent development in geometry and topology
• Gives access to sophisticated techniques in geometric analysis
• Leads to future directions of research in geometry and topology