Some Inequalities for the Lp-polar Curvature Images of Star Bodies

LI Xin-hong, MA Tong-yi

doi:10.13371/j.cnki.chin.q.j.m.2016.04.003

Chinese Quarterly Journal of Mathematics >

2016 , Vol. 31 >Issue 4: 349 - 358

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.04.003

Some Inequalities for the L_p-polar Curvature Images of Star Bodies

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College of Mathematics and Statistics,Northwest Normal University. College of Mathematics and Statistics,Hexi University

LI Xin-hong(1986-), female, native of Lanzhou, Gansu, a postgradute of Northwest Normal University, engages in convex geometric analysis and geometric inequality theory; MA Tong-yi(1959-), male, native of Huining, Gansu, a professor of Hexi University, M.S.D., engages convex geometric analysis, distance geometry, discrete geometry and inequality theory.

Received date: 2014-05-30

Online published: 2020-10-30

Supported by

Supported by the National Natural Science Foundation of China(11161019)；

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Abstract

Zhu,Lü and Leng extended the concept of L_p-polar curvature image. We continuously study the L_p-polar curvature image and mainly expound the relations between the volumes of star bodies and their L_p-polar curvature images in this article. We first establish the L_p-affine isoperimetric inequality associated with L_p-polar curvature image. Secondly,we give a monotonic property for L_p-polar curvature image. Finally, we obtain an interesting equation related to L_p-projection body of L_p-polar curvature image and L_p-centroid body.

Key words： star bodies; convex bodies; L_p-curvature image; L_p-polar curvature image

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LI Xin-hong, MA Tong-yi . Some Inequalities for the L_p-polar Curvature Images of Star Bodies[J]. Chinese Quarterly Journal of Mathematics, 2016 , 31(4) : 349 -358 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.04.003

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