Parabolic NTA domains in ${\mathbb{R}}^2$

Abstract

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 Nyström (Duke Math J. 2004).

12 pages, 2 figures. This version has minor revisions as suggested by a referee