The Lp dual Minkowski problem for p > 1 and q > 0

General L-p dual curvature measures have recently been introduced by Lutwak, Yang and Zhang [24]. These new measures unify several other geometric measures of the Brunn-Minkowski theory and the dual Brunn-Minkowski theory. L-p dual curvature measures arise from qth dual intrinsic volumes by means of Alexandrov-type variational formulas. Lutwak, Yang and Zhang [24] formulated the L-p dual Minkowski problem, which concerns the characterization of L-p dual curvature measures. In this paper, we solve the existence part of the L-p dual Minkowski problem for p > 1 and q > 0, and we also discuss the regularity of the solution. (C) 2018 Elsevier Inc. All rights reserved.