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Abstract <p> 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 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L_p\)</EquationSource> </InlineEquation>-Brunn–Minkowski inequality. In this paper, we extend Cifre and Nicolas’s result to <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(q\)</EquationSource> </InlineEquation>-quermassintegrals form. Further, as the applications of this result, we separately give the <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(q\)</EquationSource> </InlineEquation>-quermassintegrals form of the <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(L_p\)</EquationSource> </InlineEquation>-dual Brunn–Minkowski inequality and the extremums of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(q\)</EquationSource> </InlineEquation>-quermassintegrals of the polar asymmetric <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(L_p\)</EquationSource> </InlineEquation>-difference bodies. </p>

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\(q\)-Quermassintegrals Form of the Polar Duality of \(L_p\)-Brunn–Minkowski Inequality and the Applications

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Weidong Wang

摘要

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 \(L_p\) -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 \(L_p\) -dual Brunn–Minkowski inequality and the extremums of \(q\) -quermassintegrals of the polar asymmetric \(L_p\) -difference bodies.