Geometry and Topology of Manifolds

1. Front Matter

   Pages i-xii

   PDF

2. Minimal Legendrian Surfaces in the Five-Dimensional Heisenberg Group

   • Reiko Aiyama, Kazuo Akutagawa

   Pages 1-13

3. Gluing Principle for Orbifold Stratified Spaces

   • Bohui Chen, An-Min Li, Bai-Ling Wang

   Pages 15-57

4. Applications of the Affine Structures on the Teichmüller Spaces

   • Kefeng Liu, Yang Shen, Xiaojing Chen

   Pages 59-79

5. Critical Points of the Weighted Area Functional

   • Qing-Ming Cheng

   Pages 81-96

6. A New Look at Equivariant Minimal Lagrangian Surfaces in \({\mathbb {C}} P^2\)

   • Josef F. Dorfmeister, Hui Ma

   Pages 97-125

7. A Survey on Balanced Metrics

   • Jixiang Fu

   Pages 127-138

8. Can One Hear the Shape of a Group?

   • Koji Fujiwara

   Pages 139-146

9. Differential Topology Interacts with Isoparametric Foliations

   • Chao Qian, Jianquan Ge

   Pages 147-157

10. Unobstructed Deformations of Generalized Complex Structures Induced by \(C^{\infty } \) Logarithmic Symplectic Structures and Logarithmic Poisson Structures

    • Ryushi Goto

    Pages 159-183

11. The Symplectic Critical Surfaces in a Kähler Surface

    • Xiaoli Han, Jiayu Li, Jun Sun

    Pages 185-193

12. Some Evolution Problems in the Vacuum Einstein Equations

    • Junbin Li, Xi-Ping Zhu

    Pages 195-210

13. Willmore 2-Spheres in \(S^n\): A Survey

    • Xiang Ma, Peng Wang

    Pages 211-233

14. The Yau-Tian-Donaldson Conjecture for General Polarizations, I

    • Toshiki Mabuchi

    Pages 235-245

15. Behavior of Gaussian Curvature and Mean Curvature Near Non-degenerate Singular Points on Wave Fronts

    • L. F. Martins, K. Saji, M. Umehara, K. Yamada

    Pages 247-281

16. The Calabi Invariant and Central Extensions of Diffeomorphism Groups

    • Hitoshi Moriyoshi

    Pages 283-297

17. Concentration, Convergence, and Dissipation of Spaces

    • Takashi Shioya

    Pages 299-314

18. The Space of Left-Invariant Riemannian Metrics

    • Hiroshi Tamaru

    Pages 315-326

19. Futaki Invariant and CM Polarization

    • Gang Tian

    Pages 327-348

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.

• 53CXX
• Kahler manifold
• Riemannian manifold
• minimal submanifold
• symplectic manifold
• partial differential equations

• The University of Tokyo, Meguro-ku, Japan

  Akito Futaki

• Mathematical Institute, Tohoku University, Sendai,Aoba-ku, Japan

  Reiko Miyaoka

• School of Mathematical Sciences, Beijing Normal University, Beijing, China

  Zizhou Tang

• Chern Institute of Mathematics, Nankai University, Tianjin, China

  Weiping Zhang

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