A classification of $\operatorname{SL}(n)$ invariant valuations
A classification of $\operatorname{SL}(n)$ invariant valuations
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DOI：
10.4007/annals.2010.172.1219
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发表时间：
2010-08
影响因子：
4.9
通讯作者：
M. Ludwig;M. Reitzner
中科院分区：
文献类型：
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作者：
M. Ludwig;M. Reitzner
在n维凸体空间上建立了上半连续赋值和SL(N)不变赋值的分类。得到了中心仿射表面积和L仿射表面积的完全刻画。这些证明利用了一种新的凸体SL(N)整形过程。
A classification of upper semicontinuous and SL(n) invariant valuations on the space of n-dimensional convex bodies is established. As a consequence, complete characterizations of cen t ro-affine and L p affine surface areas are obtained. The proofs make use of a new SL(n) shaping process for convex bodies.