R638, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 638室)
Some Known Results of the Stable Solution in J-flow
Chao-Ming Lin (University of California, Irvine)
Abstract:
The J-flow was introduced by Donaldson [1] from the point of view of moment maps, as well as Chen [2] in his study of the Mabuchi energy. In [3], Song and Weinkov showed that the stable solution of the J-flow is equivalent to a positivity condition. Unfortunately, it is hard to check this condition, thus in [4], Lejmi and Szekelyhidi proposed a numerical positive condition, which is conjectured to be equivalent to the stable solution. In this talk, I will try to show the existence of stable solution in some simple cases and try to give some insights into a constraint which is related to Donaldson-Futaki type invariant.
Reference:
1.Moment maps and Diffeomorphisms — Simon Donaldson
2.A new Parabolic flow in Kahler Manifolds — Xiuxiong Chen
3.On the convergence and singularities of the J-flow with applications to the Mabuchi energy — Jian Song and Ben Weinkov
4.The J-flow and Stability — Mehdi Lejmi and Gabor Szekelyhidi