Abstract. An important question about ane skeletons is the existence of dierential equations that are related to the Ane Distance and the Area Distance (hence to ane skeletons) in the same way the Eikonal equation is related to the Euclidean Distance (and the medial axis). We show a surprisingly simple nonlinear second order PDE of Monge-Ampère type that relates to the ane skeletons (and extends the Eikonal equation for the medial axis). We also discuss some consequences and ideas that this new PDE formulation suggests.
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