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We study the linearized Fopl - von Karman theory of a long, thin rectangularelastic membrane that is bent through an angle $2 \alpha$. We prove rigorousbounds for the minimum energy of this configuration in terms of the platethickness $\sigma$ and the bending angle. We show that the minimum energyscales as $\sigma^{5/3} \alpha^{7/3}$. This scaling is in sharp contrast withpreviously obtained results for the linearized theory of thin sheets withisotropic compression boundary conditions, where the energy scales as $\sigma$.Comment: 15 pages, 2 figures, iopart style files; Changes - 10/25 -- Changes  to the introduction, fixed the reference

Lower bounds for the energy in a crumpled elastic sheet—a minimal ridge