Corona Decompositions for Parabolic Uniformly Rectifiable Sets

We prove that parabolic uniformly rectifiable sets admit (bilateral) corona decompositions with respect to regular Lip(1,1/2) graphs. Together with our previous work, this allows us to conclude that if Σ⊂ℝ^n+1 is parabolic Ahlfors-David regular, then the following statements are equivalent. Σ is parabolic uniformly rectifiable. Σ admits a corona decomposition with respect to regular Lip(1,1/2) graphs. Σ admits a bilateral corona decomposition with respect to regular Lip(1,1/2) graphs. Σ is big pieces squared of regular Lip(1,1/2) graphs.