Discrete taut strings and real interpolation

Classical taut strings and their multidimensional generalizations appear in a broad range of applications. In this paper we suggest a general approach based on the K-functional of real interpolation that provides a unifying framework of existing theories and extend the range of applications of taut strings. More exactly, we introduce the notion of invariant K-minimal sets, explain their connection to taut strings and characterize all bounded, closed and convex sets in Rn that are invariant K-minimal with respect to the couple (ℓ1,ℓ∞).