Characterizing addition of convex sets by polynomiality of volume and by the homothety operation
Characterizing addition of convex sets by polynomiality of volume and by the homothety operation
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通过体积多项式和拟似运算来表征凸集的加法
DOI：
10.1142/s0219199714500229
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发表时间：
2015
影响因子：
1.6
通讯作者：
Liran Rotem
中科院分区：
文献类型：
--
作者：
V. Milman;Liran Rotem
我们研究凸集之间的加法运算。我们证明，在一个简短的自然假设列表下，只有Minkowski加法具有体积的多项式性。我们还给出了另外两个表征定理。对于第一个定理，我们定义了加法运算的诱导同伦，并用这个同伦来描述加法。第二个定理描述了满足一系列自然条件的所有加法。
We study addition operations between convex sets. We show that, under a short list of natural assumptions, one has polynomiality of volume only for the Minkowski addition. We also give two other characterization theorems. For the first theorem we define the induced homothety of an addition operation, and characterize additions by this homothety. The second theorem characterizes all additions which satisfy a short list of natural conditions.