The L p dual Minkowski problem about 0 < p < 1 and q > 0

Abstract

Abstract The ( p , q p,q )-th dual curvature measures and the L p {L}_{p} dual Minkowski problem were recently introduced by Lutwak, Yang, and Zhang. In this paper, we give a solution to the existence part of the L p {L}_{p} dual Minkowski problem about 0 < p < 1 0\lt p\lt 1 and q > 0 q\gt 0 for arbitrary measures. This fills up previously obtained results.