Published Paper
Inserted: 1 dec 2020
Last Updated: 12 apr 2026
Journal: Proc. Roy. Soc. Edinburgh Sect. A
Volume: 156
Number: 2
Pages: 397-435
Year: 2026
Abstract:
We show that any isometric immersion of a flat plane domain into $\R^3$ is developable provided it enjoys $C^{1,\alpha}_{loc}$ H\"older regularity for some $\alpha>2/3$. The proof is based on showing the existence of a weak notion of second fundamental form for such immersions, the analysis of the Gauss-Codazzi-Mainardi equations in this weak setting, and a parallel result on the very weak solutions to the Monge-Amp\`ere equation which appeared in \cite{lepamonge}.
Download: