Is it possible to define mean curvature around bend/kink e.g. edge of a cube?
I take piece of paper (X-Y plane ) and bend it along a line (Y axis) it by angle $\theta$. Since this bend can be seen as a cylinder with zero radius, I would naively think that mean curvature diverges. But then this implies that it doesn’t depend on $\theta$, which also seems bit counter-intuitive.