Geometry and Topology of Manifolds: 10th China-Japan Conference 2014

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Akito Futaki, Reiko Miyaoka, Zizhou Tang, Weiping Zhang
Springer, Jun 3, 2016 - Mathematics - 348 pages
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

Minimal Legendrian Surfaces in the FiveDimensional Heisenberg Group
1
Gluing Principle for Orbifold Stratified Spaces
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

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