Conic K\"{a}hler-Einstein metrics along simple normal crossing divisors   on Fano manifolds
  We prove that on one K\"{a}hler-Einstein Fano manifold without holomorphic vector fields, there exists a unique conical K\"{a}hler-Einstein metric along a simple normal crossing divisor with admissible prescribed cone angles. We also establish a curvature estimate for conic metrics along a simple normal crossing divisor which generalizes Li-Rubinstein's estimate and derive high order estimates from this estimate. 
Aijin Lin, Liangming Shen
math.DG