Extremal function of intrinsic norms
  Through the study of the degenerate complex Monge-Amp\`ere equation, we establish the optimal regularity of the extremal function associated to intrinsic norms of Chern-Levine-Nirenberg and Bedford-Taylor. We prove a conjecture of Chern-Levine-Nirenberg on the extended intrinsic norms on complex manifolds and verify Bedford-Taylor's representation formula for these norms in general. 
Pengfei Guan