Abstract
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.
Funding Statement
The research of Yong Huang is supported by NSFC grants 12171144 and 12231006.
The research of Jiaqian Xi is supported by the National Natural Science Foundation of China (12071277), and by the STSCM program (20JC1412600).
The research of Zhao is supported in part by the U.S. National Science Foundation Grant DMS-2132330.
Citation
Yong Huang. Jiaqian Liu. Dongmeng Xi. Yiming Zhao. "Dual curvature measures for $\log$-concave functions." J. Differential Geom. 128 (2) 815 - 860, October 2024. https://doi.org/10.4310/jdg/1727712894
Information
