We show the surprising results that while the local reach of the boundary of an minimizer is bounded below by , the global reach can be smaller. We do this by demonstrating several example minimizing sets not equal to the union of the -balls they contain.
"There Are Thin Minimizers of the L1TVFunctional." Abstr. Appl. Anal. 2012 1 - 8, 2012. https://doi.org/10.1155/2012/930978