In the Minkowski Problem, a function is given on unit vectors and the conditions this function has to satisfy in order for it to be the Gaussian curvature on the normals of some strictly convex, compact hypersurface is of interest. This problem has been thoroughly studied by geometers and is also related to Monge-Ampere equations and translation of radar information. Construction of the surfaces given valid data, however, can be difficult. We present here a geometrically based flow that produces these surfaces in steady state. The algorithm used is based on the level set method and numerical results show we are able to construct the many different shapes that arise from the Minkowski Problem.
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