Georgia Institute of Technology College of Sciences

We revisit the classical problem of constructing a developable surface along a given Frenet curve $\gamma$ in space. First, we generalize a well-known formula, introduced in the literature by Sadowsky in 1930, for the Willmore energy of the rectifying developable of $\gamma$ to any (infinitely narrow) flat ribbon along the same curve. Then we apply the direct method of the calculus of variations to show the existence of a flat ribbon along $\gamma$ having minimal bending energy. Joint work with Simon Blatt.