论文标题
$ \ Mathbb {r}^n $的$ M $ ellipsoids的Minkowski和$ m $ eLLIPSOID的封闭形式参数方程
Closed-Form Parametric Equation for the Minkowski Sum of $m$ Ellipsoids in $\mathbb{R}^N$ and Associated Volume Bounds
论文作者
论文摘要
审查凸体的一般结果并用于得出$ m $ nutipary椭圆形的Minkowski总和边界的精确闭合形式的参数公式。还得出了这些Minkowski总和的主要曲率的表达式。然后将这些结果用于获得椭圆形矩阵的椭圆形和下部体积的界限。下限比Brunn-Minkowski的不平等更明显。还给出了凸体的反向等距不等式。
General results on convex bodies are reviewed and used to derive an exact closed-form parametric formula for the Minkowski sum boundary of $m$ arbitrary ellipsoids in $N$-dimensional Euclidean space. Expressions for the principal curvatures of these Minkowski sums are also derived. These results are then used to obtain upper and lower volume bounds for the Minkowski sum of ellipsoids in terms of their defining matrices; the lower bounds are sharper than the Brunn-Minkowski inequality. A reverse isometric inequality for convex bodies is also given.
