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Bending surfaces in Riemannian manifolds Why is the half-torus rigid?Is a smooth closed surface in Euclidean 3-space rigid?Riemannian surfaces with an explicit distance function?Is a rhombus rigid on a sphere or torus? And generalizationsIsometric embedding a convex cap to render its boundary planarWhy is the half-torus rigid?Geodesic circles on riemannian manifoldsTweetable way to see that Willmore energy is Möbius invariant?Alexandrov angles in Riemannian manifoldsIntrinsic vs Extrinsic geometry of convex surfacesWhat is known about sufficient conditions for the rigidity of a convex surface?Pogorelov's rigidity theorem vs Cohn-Vossen rigidity theorem 4 1 $begingroup$ Let $S$ be an immersed surface in $mathbbR^3$ (with the flat metric). We will call it flexible if there exists a smooth (or whatever regular) family of immersions $s_t: Sto mathbbR^3$ , such that each $s_t$ induces the same metric on $S$ and no $s_t_1$ and $s_t_2$ are related by an isometry of $