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<p>The variational formula for Orlicz moments with respect to the Asplund sum in the class of log-concave functions is established. Such a variational formula naturally leads to a family of dual Orlicz curvature measures for log-concave functions. These are functional analogs of dual (Orlicz) curvature measures for convex bodies. Partial existence results for the functional dual Orlicz Minkowski problem are shown.</p>

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Dual Orlicz curvature measures for log-concave functions and their Minkowski problems

  • 期刊论文

  • 发表日期：

    2025年1月6日

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  • Niufa Fang,
  • Deping Ye,
  • Zengle Zhang,
  • Yiming Zhao

摘要

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