A curvature flow to the Lp Minkowski-type problem of q-capacity

Abstract

Abstract This article concerns the L p {L}_{p} Minkowski problem for q-capacity. We consider the case p ≥ 1 p\ge 1 and 1 < q < n 1\lt q\lt n in the smooth category by a kind of curvature flow, which converges smoothly to the solution of a Monge-Ampére type equation. We show the existence of smooth solution to the problem for p ≥ n p\ge n . We also provide a proof for the weak solution to the problem when p ≥ 1 p\ge 1 , which has been obtained by Zou and Xiong.