Mixed Measures of Convex Cylinders and Quermass Densities of Boolean Models
Mixed Measures of Convex Cylinders and Quermass Densities of Boolean Models
复制标题
布尔模型的凸柱体和Quermass密度的混合测量
DOI：
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发表时间：
2009
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通讯作者：
L. Hoffmann
中科院分区：
文献类型：
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作者：
L. Hoffmann
Schneider和Weil通过引入凸体的混合测度，得到了凸体曲率测度的平移积分公式。由于混合测度是局部定义的，这些结果可以推广到任意闭凸集。此外，迭代版本的这些公式，由于韦伊被用于Fallert介绍quermass密度（非平稳和非各向同性）泊松过程的凸体和相应的布尔模型。本文首先计算了凸柱面混合测度的特殊形式，并证明了其平移积分公式。在适应一些结果的混合措施的凸体到这个设置，然后我们使用这个积分公式获得quermass密度（非平稳和非各向同性）泊松过程的凸柱。此外，凸圆柱体的布尔模型的quermass密度表示的基础泊松过程的混合密度推广经典公式由Davy和Spiess和Spodarev最近的结果。
Translative integral formulas for curvature measures of convex bodies were obtained by Schneider and Weil by introducing mixed measures of convex bodies. These results can be extended to arbitrary closed convex sets since mixed measures are locally defined. Furthermore, iterated versions of these formulas due to Weil were used by Fallert to introduce quermass densities for (non-stationary and non-isotropic) Poisson processes of convex bodies and respective Boolean models. In the present paper, we first compute the special form of mixed measures of convex cylinders and prove a translative integral formula for them. After adapting some results for mixed measures of convex bodies to this setting we then use this integral formula to obtain quermass densities for (non-stationary and non-isotropic) Poisson processes of convex cylinders. Furthermore, quermass densities of Boolean models of convex cylinders are expressed in terms of mixed densities of the underlying Poisson process generalizing classical formulas by Davy and recent results by Spiess and Spodarev.