Geometry and Topology of Manifolds

Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincaré conjecture, the YauTianDonaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among others, the StromingerYauZaslow conjecture on mirror symmetry, the relative YauTianDonaldson 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.

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 Includes supplementary material: sn.pub/extras