We provide a curvature flow approach to the regular Christoffel-Minkowski problem. The speed of our is an entropy preserving type and contains global term.

A balanced word is one in which any two factors of the same length contain the same number of each letter of the alphabet up to one. Finite binary balanced words are called Sturmian words. A Sturmian word is bispecial if it can be extended to the left and to the right with both letters remaining a Sturmian word. There is a deep relation between bispecial Sturmian words and Christoffel words, th...

We introduce and study natural derivatives for Christoffel and finite standard words, as well as for characteristic Sturmian words. These derivatives, which are realized as inverse images under suitable morphisms, preserve the aforementioned classes of words. In the case of Christoffel words, the morphisms involved map a to ak+1b (resp., abk) and b to akb (resp., abk+1) for a suitable k > 0. As...