Geometry of Ricci solitons on complex manifolds

(1)在一个联合工作（东北数学）。J., 65, 2013, 243-252)与Y. Nakagawa，我们将Sakane-Koiso的Kaehler-Einstein度量构造推广到Futaki不变量不消失的Kaehler-Ricci孤子。在这种情况下，我们获得Sasaki-Einstein度量来代替Kaehler-Einstein度量。(2)对于复射影平面在3个非共线点上的爆破上的Kaehler-Einstein度规，通过对实2平面上有界区域上双曲仿射球方程解的渐近展开，得到了其详细描述。数学学报，48,219-229)。(3)对于Donaldson-Tian-Yau猜想，我们证明了：i)渐近相对Chow稳定性暗示了多平衡度量序列的存在（Osaka J. Math. 48, 2011, 845-856）；ii)强相对k稳定性意味着渐近相对Chow稳定性（与Y.Nitta联合研究）。

(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).