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April 3, 2026Mathematical Notes0 citations

q-Quermassintegrals Form of the Polar Duality of Lₚ-Brunn–Minkowski Inequality and the Applications

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WWW. D. Wang

Key Points

  • This research aims to extend the quermassintegrals form of the polar duality of the L_p-Brunn–Minkowski inequality to the q-quermassintegrals form.
  • Extension of previous results by Cifre and Nicolas to q-quermassintegrals
  • Application of results to the L_p-dual Brunn–Minkowski inequality
  • Analysis of extremums of q-quermassintegrals for polar asymmetric L_p-difference bodies
  • Established the q-quermassintegrals form of the L_p-dual Brunn–Minkowski inequality
  • Identified extremums for q-quermassintegrals related to polar asymmetric L_p-difference bodies

Abstract

The quermassintegrals form of the polar duality of Brunn–Minkowski inequality was established by Firey. In 2016, Cifre and Nicolas gave the quermassintegrals form of the polar duality of Lₚ -Brunn–Minkowski inequality. In this paper, we extend Cifre and Nicolas’s result to q -quermassintegrals form. Further, as the applications of this result, we separately give the q -quermassintegrals form of the Lₚ -dual Brunn–Minkowski inequality and the extremums of q -quermassintegrals of the polar asymmetric Lₚ -difference bodies.

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Cite This Study

W. D. Wang (2025) studied this question.

synapsesocial.com/papers/69cf5e745a333a821460cd6ehttps://doi.org/10.1134/s0001434625602655
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