In this paper we show by example that there is no uniform estimate for the L p -Minkowski problem. As a result we obtain the nonuniqueness of solutions to the problem.
In this paper the dual Orlicz-Minkowski problem, a generalization of the L p dual Minkowski problem, is studied. By studying a flow involving the Gauss curvature and support function, we obtain a new existence result of solutions to this problem for smooth measures.
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