We introduce dual curvature measures for log-concave functions, which in the case of characteristic functions recover the dual curvature measures for convex bodies introduced by Huang-Lutwak-Yang-Zhang in 2016. Variational formulas are shown. The associated Minkowski problem for these dual curvature measures is considered and sufficient conditions in the symmetric setting are demonstrated.
@article{arxiv.2210.02359,
title = {Dual curvature measures for log-concave functions},
author = {Yong Huang and Jiaqian Liu and Dongmeng Xi and Yiming Zhao},
journal= {arXiv preprint arXiv:2210.02359},
year = {2023}
}