MiS Preprint Repository

In this paper, we consider the model case when the compact set $K$ is contained in the hyperboloid $H_{-1}$, which is a subset of symmetric $2\times 2$ matrices. The hyperboloid $H_{-1}$ is generated by two families of rank-one lines and related to the hyperbolic Monge-Ampere equation $det{\mathrm{\nabla }}^{2}u=-1$. For some compact subsets $K$ containing rank-one connection, we show the rigidity property of $K$ by imposing proper topology for the convergence of approximate solutions and affine boundary conditions.