Convergence of general inverse $\sigma_k$-flow on K\"{a}hler manifolds   with Calabi Ansatz
  We study the convergence behavior of the general inverse $\sigma_k$-flow on K\"{a}hler manifolds with initial metrics satisfying the Calabi Ansatz. The limiting metrics can be either smooth or singular. In the latter case, interesting conic singularities along negatively self-intersected sub-varieties are formed as a result of partial blow-up. 
Hao Fang and Mijia Lai
math.DG math.AP