AdS/CFT correspondence and GIT stablity

建立了环形Sasaki-Einstein度量的一般存在性结果。作为它的应用，在环面范诺流形的正则线束上构造了Kaehler Ricci流的永恒解。在具有非离散自同构的极化流形上，证明了存在阻碍渐近Chow半稳定的积分不变量。利用它们可以证明一个渐近不稳定的环形法诺-凯勒-爱因斯坦流形的存在性。S.K.Donaldson证明了具有常标量曲率和离散自同构的极化流形是渐近周稳定的。得到了紧缩Ricci孤子的普遍下直径界。

A general existence result of toric Sasaki-Einstein metrics was established. As its application, an eternal solution of Kaehler Ricci flow was constructed on the canonical line bundle of toric Fano Manifolds.On polarized manifolds with non-discrete automorphisms, it is shown that there are integral invariants which obstruct asymptotic Chow semi-stability. Using them it is possible to show the existence of a toric Fano Kaehler-Einstein manifold which is asymptotically unstable. It has been shown by S.K.Donaldson that a polarized manifolds with constant scalar curvature and with discrete automorphisms is asymptotically Chow-stable.A universal lower diameter bound for compact shrinking Ricci solitons was obtained.