Abstract
We study closed sets F SUBSET OF Rd whose distance function dF:=dist(., F)is DC (i.e., is the difference of two convex functions on Rd). Our main result asserts that if FSUBSET OF R2 is a graph of a DC function g:R -> R, then Fhas the above property.
If d >1, the same holds if g:Rd-1 -> Ris semiconcave, however the case of a general DC function gremains open.