English

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

Metric Geometry 2023-03-21 v1

Abstract

In this paper, we derive the continuity of solutions to the LpL_{p} torsional Minkowski problem for p>1p>1. It is shown that the weak convergence of the LpL_{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 LpL_{p} torsional Minkowski problem with regard to pp is also obtained.

Keywords

Cite

@article{arxiv.2303.11038,
  title  = {On the continuity of the solutions to the $L_{p}$ torsional Minkowski problem},
  author = {Jinrong Hu and Qiongfang Mao and Sinan Wang},
  journal= {arXiv preprint arXiv:2303.11038},
  year   = {2023}
}