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<p>We extend Grinberg’s and Schneider’s intersection inequalities, which provide bounds on the volume of a body in Euclidean space based on its intersections with lower-dimensional flats, to a functional context. Our results establish analogous inequalities for specific norms and the dual affine quermassintegral of functions.</p>

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Functional Extensions of Grinberg’s and Schneider’s Intersection Inequalities

  • 期刊论文

  • 发表日期：

    2025年6月14日

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  • Songjun Lv

摘要

We extend Grinberg’s and Schneider’s intersection inequalities, which provide bounds on the volume of a body in Euclidean space based on its intersections with lower-dimensional flats, to a functional context. Our results establish analogous inequalities for specific norms and the dual affine quermassintegral of functions.