Scholarlink

<p>In this paper, we prove that the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(L_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation>-support function of the shadow system <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(K_t\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mi>t</mi> </msub> </math></EquationSource> </InlineEquation> is convex and the volume of the projection of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(L_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> polar bodies of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(K_t\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mi>t</mi> </msub> </math></EquationSource> </InlineEquation> is <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\frac{1}{n-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <mfrac> <mn>1</mn> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> </math></EquationSource> </InlineEquation>-concave with respect to parameter <i>t</i>, and obtain some related inequalities. Finally, we present the reverse Rogers-Shephard type inequality for <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(L_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation>-polar bodies.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The \(L_p\) Polar bodies of shadow system and related inequalities

  • 期刊论文

  • 发表日期：

    2026年4月15日

查看全文
  • Lujun Guo,
  • Hanxiao Wang

摘要

In this paper, we prove that the \(L_p\) L p -support function of the shadow system \(K_t\) K t is convex and the volume of the projection of \(L_p\) L p polar bodies of \(K_t\) K t is \(\frac{1}{n-1}\) 1 n - 1 -concave with respect to parameter t, and obtain some related inequalities. Finally, we present the reverse Rogers-Shephard type inequality for \(L_p\) L p -polar bodies.