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

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### Contents

1 | |

15 | |

Applications of the Affine Structures on the Teichmüller Spaces | 59 |

Critical Points of the Weighted Area Functional | 81 |

A New Look at Equivariant Minimal Lagrangian Surfaces in mathbbC P2 | 97 |

A Survey on Balanced Metrics | 127 |

Can One Hear the Shape of a Group? | 139 |

Differential Topology Interacts with Isoparametric Foliations | 147 |

Some Evolution Problems in the Vacuum Einstein Equations | 195 |

A Survey | 211 |

The YauTianDonaldson Conjecture for General Polarizations I | 235 |

Behavior of Gaussian Curvature and Mean Curvature Near Nondegenerate Singular Points on Wave Fronts | 247 |

The Calabi Invariant and Central Extensions of Diffeomorphism Groups | 283 |

Concentration Convergence and Dissipation of Spaces | 299 |

The Space of LeftInvariant Riemannian Metrics | 315 |

Futaki Invariant and CM Polarization | 327 |

Unobstructed Deformations of Generalized Complex Structures Induced by Cinfty Logarithmic Symplectic Structures and Logarithmic Poisson Stru... | 159 |

The Symplectic Critical Surfaces in a Kähler Surface | 185 |

### Other editions - View all

Geometry and Topology of Manifolds: Shanghai, China, September 2014 Akito Futaki,Reiko Miyaoka,Zizhou Tang,Weiping Zhang No preview available - 2016 |

### Common terms and phrases

2-spheres adjoint transform balanced metric Calabi Calabi–Yau manifolds canonical cohomology groups compact complex manifold complex structure Corollary curve defined Definition deformations denote diffeomorphism equations equivariant equivariant minimal Lagrangian Euler class exists function Futaki invariant Gauss map Gaussian curvature Geom geometry given gluing datum gluing map harmonic maps Hermitian holomorphic horocycle horocycle structures hypersurface immersion induced initial data isomorphism isoparametric foliations Kähler Kähler manifold Legendrian Lemma Lie algebra Lie algebroid Lie groupoid Lie groups line bundle logarithmic Math Mathematics mean curvature mean curvature flow Mg,n minimal Lagrangian surface minimal surfaces mm-spaces moduli space n-dimensional non-degenerate normal null obtain orbifold orbifold gluing period map proof Proposition proved Riemannian manifolds Riemannian metrics Rn+1 satisfies self-shrinkers singular point smooth sphere stratified space submanifold subset Teichmüller space Theorem Topology Torelli space translationally equivariant minimal vector field Willmore surfaces