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On the continuity of the solutions to the L_(p) torsional Minkowski problem
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On the continuity of the solutions to the L_(p) torsional Minkowski problem
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In this paper, we derive the continuity of solutions to the $L_{p}$ torsional Minkowski problem for $p>1$. It is shown that the weak convergence of the $L_{p}$ torsional measure implies the convergence of the sequence of the corresponding convex bodies in the Hausdorff metric. Furthermore, continuity of the solution to the $L_{p}$ torsional Minkowski problem with regard to $p$ is also obtained.
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