Parabolic NTA domains in $\mathbb R^2$
  We show that each connected component of the boundary of a parabolic NTA domain in $\mathbb R^2$ is given by a graph. We then apply this observation to classify blowup solutions in $\mathbb R^2$ to a free boundary problem for caloric measure first considered by Hofmann, Lewis and Nystr\"om (Duke Math J. 2004). 
Max Engelstein
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