AI 中文总结
该研究证明非紧李维数为n的单模局部紧群满足严格非阿贝尔布伦-闵可夫斯基不等式，建立了一般形式并证实相关猜想，还应用得到非紧型对称空间的等周不等式。
AI 中文摘要
我们证明了每个非紧李维数为n的单模局部紧群G都满足严格的布伦-闵可夫斯基不等式：μ_G(XY)^(1/n)≥μ_G(X)^(1/n)+μ_G(Y)^(1/n)，并为任意可能非单模的局部紧群建立了一般形式，这完全证实了我们与Zhang提出的非阿贝尔布伦-闵可夫斯基猜想，作为应用，我们得到了非紧型对称空间上的等周不等式。
英文摘要
We prove that every unimodular locally compact group $G$ of noncompact Lie dimension $n$ satisfies the sharp Brunn--Minkowski inequality \[ μ_G(XY)^{1/n}\geμ_G(X)^{1/n}+μ_G(Y)^{1/n}, \] and establish a general form for arbitrary, possibly nonunimodular, locally compact groups. This fully confirms the nonabelian Brunn--Minkowski conjecture proposed by the present authors and Zhang. As an application, we obtain an isoperimetric inequality on symmetric spaces of noncompact type.
Comments28 pages
