WANG Wei-dong, LENG Gang-song. Inequalities Relating to Lp-Version of the Petty’s Conjectured Projection Inequality[J]. Applied Mathematics and Mechanics, 2007, 28(2): 245-252.
Citation: WANG Wei-dong, LENG Gang-song. Inequalities Relating to Lp-Version of the Petty’s Conjectured Projection Inequality[J]. Applied Mathematics and Mechanics, 2007, 28(2): 245-252.

Inequalities Relating to Lp-Version of the Petty’s Conjectured Projection Inequality

  • Received Date: 2005-06-27
  • Rev Recd Date: 2006-11-30
  • Publish Date: 2007-02-15
  • Petty's conjectured projection inequality is a famous open problem in convex bodies theory.It was shown that an inequality relating to Lp-version of the Petty's conjectured projection inequality by using the notions of the Lp-mixed volume and the Lp-dual mixed volume,the relation of the Lp-projection body and the geometric body Г-pK,the Bourgain-Milman inequality and the Lp-Busemann-Petty inequality.In addition,for each origin-symmetric convex body,applying the Jensen inequality and the monotonicity of the geometric body Г-pK,the reverses of Lp-version of the Petty's conjectured projection inequality and the Lp-Petty projection inequality were given respectively.
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