There are Thin Minimizers of the L1TV Functional
  In this paper we show the surprising results that while the local reach of the boundary of an L1TV minimizer is bounded below by 1/lambda, the global reach can be smaller. We do this by demonstrating several example minimizing sets not equal to the union of the 1/lambda -balls they contain. 
Benjamin Van Dyke and Kevin R. Vixie
math.CA math.OC