The $L_p$ dual Minkowski problem for $p>1$ and $q>0$
Analysis of PDEs
2026-04-23 v5
Abstract
General dual curvature measures have recently been introduced by Lutwak, Yang and Zhang. These new measures unify several other geometric measures of the Brunn-Minkowski theory and the dual Brunn-Minkowski theory. dual curvature measures arise from th dual inrinsic volumes by means of Alexandrov-type variational formulas. Lutwak, Yang and Zhang formulated the dual Minkowski problem, which concerns the characterization of dual curvature measures. In this paper, we solve the existence part of the dual Minkowski problem for and , and we also discuss the regularity of the solution.
Keywords
Cite
@article{arxiv.1802.00933,
title = {The $L_p$ dual Minkowski problem for $p>1$ and $q>0$},
author = {Károly J. Böröczky and Ferenc Fodor},
journal= {arXiv preprint arXiv:1802.00933},
year = {2026}
}