• The $L_p$-Curvature Images of Convex Bodies and $L_p$-Projection Bodies

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      https://www.ias.ac.in/article/fulltext/pmsc/118/03/0413-0424

    • Keywords

       

      𝑝-Curvature image; 𝑝-affine surface area; $L_p$-projection body; $L_p$-mixed volume; $L_p$-dual mixed volume.

    • Abstract

       

      Associated with the $L_p$-curvature image defined by Lutwak, some inequalities for extended mixed 𝑝-affine surface areas of convex bodies and the support functions of $L_p$-projection bodies are established. As a natural extension of a result due to Lutwak, an $L_p$-type affine isoperimetric inequality, whose special cases are $L_p$-Busemann–Petty centroid inequality and $L_p$-affine projection inequality, respectively, is established. Some $L_p$-mixed volume inequalities involving $L_p$-projection bodies are also established.

    • Author Affiliations

       

      Songjun Lv1 Gangsong Leng2

      1. College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, People’s Republic of China
      2. Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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