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Some inequalities for -mixed volume.

Bin Chen1, Weidong Wang1,2

  • 11Department of Mathematics, China Three Gorges University, Yichang, China.

Journal of Inequalities and Applications
|March 7, 2019
PubMed
Summary

Researchers explored new inequalities for the -mixed volume, a concept generalizing mixed volumes. This study establishes cyclic, monotonic, and product inequalities for these volumes, advancing geometric measure theory.

Keywords:
Cyclic inequalityMonotonic inequalityProduct inequality

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Area of Science:

  • Convex Geometry
  • Geometric Measure Theory

Background:

  • The -mixed volume, introduced by Lutwak, Yang, and Zhang, is a generalization of mixed volumes.
  • Special cases include the -mixed volume and the -dual mixed volume.

Purpose of the Study:

  • To establish new inequalities associated with the -mixed volumes.
  • To extend the understanding of inequalities in geometric measure theory.

Main Methods:

  • The study focuses on theoretical mathematical derivations.
  • It involves the analysis of properties of -mixed volumes.

Main Results:

  • New cyclic inequalities for -mixed volumes have been established.
  • New monotonic inequalities for -mixed volumes have been derived.
  • New product inequalities related to -mixed volumes have been proven.

Conclusions:

  • The established inequalities provide new tools for studying convex bodies.
  • This work contributes to the ongoing research in geometric inequalities.