Destabilizing objects and multiplier ideal sheaves

当蒙日-安培方程不能解时，出现乘法器理想轴。另一方面，Futaki不变量阻碍了Kahler-Einstein度量的存在，Kahler-Einstein度量的存在被简化为求解Monge-Ampere方程。因此，在乘法器理想轴和富塔基不变量之间预期有某种关系。佐野裕治和我在这个方向上得到了结果。在同样的背景下，Yuji Sano和我进行了类似的研究，得到了紧缩Ricci孤子直径的一个普适下界，这是Ricci流的自相似解。这一下界在李海忠、李向东的共同工作中得到进一步完善。

The multiplier ideal sheaves appear when the Monge-Ampere equation can not be solved. On the other hand the Futaki invariant is an obstruction to the existence of Kahler-Einstein metrics, and the existence of Kahler-Einstein metrics is reduced to solving the Monge-Ampere equation. It is therefore expected to have some relationship between the multiplier ideal sheaves and the Futaki invariant. Yuji Sano and I obtained results in this direction. As a similar research in the same context, Yuji Sano and I obtained a universal lower bound of the diameter of compact shrinking Ricci solitons, which are the self-similar solutions to the Ricci flow. This lower bound was further improved in a joint work with Hai-Zhong Li and Xiang-Dong Li.