Local Tensor Valuations
Local Tensor Valuations
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DOI：
10.1007/s00039-014-0289-0
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发表时间：
2013-09
影响因子：
2.2
通讯作者：
D. Hug;R. Schneider
中科院分区：
文献类型：
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作者：
D. Hug;R. Schneider
局部闵可夫斯基张量是欧几里德空间中凸体空间上的赋值，其值在张量测度空间中。它们同时推广了固有体积，曲率测度和等长协变闵可夫斯基张量这些张量是由McMullen引入并由Alesker描述的。与Hadwiger和Alesker的表征定理类似，我们给出了凸体上所有与局部Minkowski张量具有等距协方差和弱连续性基本几何性质的局部定义张量测度的完整分类。
The local Minkowski tensors are valuations on the space of convex bodies in Euclidean space with values in a space of tensor measures. They generalize at the same time the intrinsic volumes, the curvature measures and the isometry covariant Minkowski tensors that were introduced by McMullen and characterized by Alesker. In analogy to the characterization theorems of Hadwiger and Alesker, we give here a complete classification of all locally defined tensor measures on convex bodies that share with the local Minkowski tensors the basic geometric properties of isometry covariance and weak continuity.