On the continuity of the solutions to the $L_{p}$ torsional Minkowski problem

Jinrong Hu; Qiongfang Mao; Sinan Wang

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arXiv · 2303.11038

On the continuity of the solutions to the $L_{p}$ torsional Minkowski problem

Jinrong Hu·Qiongfang Mao·Sinan Wang

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Abstract

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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Jinrong Hu, Qiongfang Mao, Sinan Wang. 2023-03-20. On the continuity of the solutions to the $L_{p}$ torsional Minkowski problem. https://arxiv.org/abs/2303.11038

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