Developable surfaces with prescribed boundary

It is proved that a generic simple, closed, piecewise regular curve in space can be the boundary of only infinitely many developable surfaces with nonvanishing mean curvature. The relevance of this result in the context of the dynamics of developable surfaces is discussed.Research supported by project Clothilde, ERC research grant 741930, and research grants PID2019-103849GB-I00, from the Kingdom of Spain, 2017 SGR 932 from the Catalan Government. MAC is also with Institut de Robòtica i Informàtica Industrial (CSIC-UPC), the Institut de Matemàtiques de la UPC-BarcelonaTech (IMTech) and the Barcelona Graduate School of Mathematics (BGSMath).Peer ReviewedPostprint (published version