R. Kupferman

Branch points and non-density for finite-bending isometric immersions of hyperbolic surfaces

The space of $W^{2,2}$-isometric immersions of a surface into $\mathbb{R}^3$ arises naturally in the variational theory of thin elastic sheets: it is precisely the finite-bending class, where the bending energy --- the $L^2$-norm of the second fundamental form --- is finite. For sheets with negative Gaussian curvature,...