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

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.