4 problems

Let $f(u,v)$ be a smooth conjugate net, and let $(u_0,v_0)$ be a generic point. A reparametrization replaces $f(u,v)$ by $F(U,V)$ with $F(U(u),V(v))=f(u,v)$, where $U$ and $V$ have…

A flexible polyhedron is a polyhedron admitting a continuous Euclidean isometric deformation through noncongruent realizations. The bellows conjecture. The volume of a flexible pol…

Let $S$ be an analytic surface in $\mathbb R^3$. Suppose that through each point of $S$ there are two transversal arcs of isotropic circles, lying on one isotropic sphere, fully co…

Affine Scherk classification conjecture. Except for planes, the only minimal affine translation surface is the graph