Geometry of Ricci solitons on complex manifolds

(1)在联合工作（Tohoku Math. J.，65，2013，243-252）与Y. Nakagawa的方法，我们将Sakane-Koiso构造的Kaehler-Einstein度量推广到Futaki不变量不为零的Kaehler-Ricci孤子情形。在这种情况下，我们得到Sasaki-Einstein度量代替Kaehler-Einstein度量。(2)对于复射影平面在3个非共线点上爆破的Kaehler-Einstein度量，其详细描述是通过在真实的2-平面中的有界区域上的双曲仿射球方程的解的渐近展开获得的（AMS/IP Stud.Adv.Math.48，219-229）。(3)关于Donaldson-Tian-Yau猜想，我们证明了：i）渐近相对Chow稳定性蕴含着多平衡度量序列的存在性（Osaka J. Math. 48，2011，845-856）; ii）强相对K-稳定性蕴含着渐近相对Chow稳定性（与Y.Nitta的联合工作）。

(1) In a joint work (Tohoku Math. J., 65, 2013, 243-252) with Y. Nakagawa, we generalized Sakane-Koiso's construction of Kaehler-Einstein metrics to the Kaehler-Ricci soliton case where the Futaki invariant is non-vanishing. In this case, we obtain Sasaki-Einstein metrics in place of Kaehler-Einstein metrics.(2) For the Kaehler-Einstein metric on the blowing-up of the complex projective plane at 3 non-colinear points, its detailed description was obtained by asymptotic expansion of the solution of a hyperbolic affine sphere equation on a bounded domain in the real 2-plane (AMS/IP Stud. Adv. Math. 48, 219-229).(3) As to the Donaldson-Tian-Yau Conjecture, we proved: i) Asymptotic relative Chow stability implies the existence of a sequence of polybalanced metrics (Osaka J. Math. 48, 2011, 845-856); ii) strong relative K-stability implies asymptotic relative Chow stability (joint work with Y.Nitta).