<p>In this paper, we prove the Borell-Brunn-Minkowski type inequalities, which improve several inequalities in the literature, e.g. generalized Brunn-Minkowski inequality, Borell-Brascamp-Lieb inequality, and nonlinear Brunn-Minkowski inequality. We also get a functional version of Brunn’s concavity principle in spaces with bitriangular laws of composition. As an application on the Heisenberg group <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2163_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">${\mathbb {H}}^n$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>, we prove some Brunn-Minkowski type inequalities in <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2163_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">${\mathbb {H}}^n$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>, especially isomorphic versions of the conjectured Brunn-Minkowski inequality in <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2163_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">${\mathbb {H}}^n$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>. We also obtain an <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2163_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$L_p$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation>-Brunn-Minkowski inequality in measure spaces with bitriangular laws of composition.</p>

The Borell-Brunn-Minkowski Type Inequality in Spaces with Bitriangular Laws of Composition and Some Applications

期刊论文
发表日期：

2025年9月18日

查看全文

Zhen-Hui Bu,
Denghui Wu

摘要

In this paper, we prove the Borell-Brunn-Minkowski type inequalities, which improve several inequalities in the literature, e.g. generalized Brunn-Minkowski inequality, Borell-Brascamp-Lieb inequality, and nonlinear Brunn-Minkowski inequality. We also get a functional version of Brunn’s concavity principle in spaces with bitriangular laws of composition. As an application on the Heisenberg group ${\mathbb {H}}^n$ $H^{n}$ , we prove some Brunn-Minkowski type inequalities in ${\mathbb {H}}^n$ $H^{n}$ , especially isomorphic versions of the conjectured Brunn-Minkowski inequality in ${\mathbb {H}}^n$ $H^{n}$ . We also obtain an $L_p$ $L_{p}$ -Brunn-Minkowski inequality in measure spaces with bitriangular laws of composition.