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arXiv · 2309.12260

The dual Orlicz curvature measures for log-concave functions and their related Minkowski problems

Niufa Fang·Deping Ye·Zengle Zhang·Yiming Zhao
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Abstract

The variation of a class of Orlicz moments with respect to the Asplund sum within the class of log-concave functions is demonstrated. Such a variational formula naturally leads to a family of dual Orlicz curvature measures for log-concave functions. They are functional analogs of dual (Orlicz) curvature measures for convex bodies. Partial existence results for the functional dual Orlicz Minkowski problem are shown.

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Niufa Fang, Deping Ye, Zengle Zhang, Yiming Zhao. 2023-09-21. The dual Orlicz curvature measures for log-concave functions and their related Minkowski problems. https://arxiv.org/abs/2309.12260

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