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Gauge rigidity in an inverse problem for the prescribed Gaussian curvature equation
We prove uniqueness for an inverse boundary problem for the prescribed Gaussian curvature equation $\det D^2u=K(x)(1+|\nabla u|^2)^2$ on a smooth bounded simply connected planar domain. We compare smooth positive curvatures on a common open class of Dirichlet values for which the convex problems are
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