Abstract
General Lp 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. Lp dual curvature measures arise from qth dual intrinsic volumes by means of Alexandrov-type variational formulas. Lutwak, Yang and Zhang [24] formulated the Lp dual Minkowski problem, which concerns the characterization of Lp dual curvature measures. In this paper, we solve the existence part of the Lp dual Minkowski problem for p>1 and q>0, and we also discuss the regularity of the solution.
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