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MiS Preprint
53/2003
Rigidity for the hyperbolic Monge-Ampere equation
Chun-Chi Lin
Abstract
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 $\det\nabla ^{2}u=-1$. 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.
