The geometry of <i>C</i><sup>1,<i>α</i></sup> flat isometric immersions
The geometry of <i>C</i><sup>1,<i>α</i></sup> flat isometric immersions
We show that any isometric immersion of a flat plane domain into ${\mathbb {R}}^3$ is developable provided it enjoys the little Hölder regularity $c^{1,2/3}$ . In particular, isometric immersions of local $C^{1,\alpha }$ regularity with $\alpha >2/3$ belong to this class. The proof is based on the existence of a …