Polar coordinates in Carnot groups
Polar coordinates in Carnot groups
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DOI：
10.1007/s00209-002-0441-7
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发表时间：
2002-12
影响因子：
0.8
通讯作者：
Z. Balogh;J. Tyson
中科院分区：
文献类型：
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作者：
Z. Balogh;J. Tyson
我们描述了一个程序，用于构建“极坐标”在某一类卡诺群。我们表明，我们的建设可以进行海森堡型的群体，我们给出明确的公式，极坐标分解的设置。该结构利用了非线性势理论，特别是p-sub-拉普拉斯算子的基本解。作为这个结果的应用，我们得到了Moser-Trudinger不等式的精确容量估计，表示公式和一个显式的锐常数。我们还获得了拟正则映射的拓扑和测度论的结果。
We describe a procedure for constructing ”polar coordinates” in a certain class of Carnot groups. We show that our construction can be carried out in groups of Heisenberg type and we give explicit formulas for the polar coordinate decomposition in that setting. The construction makes use of nonlinear potential theory, specifically, fundamental solutions for thep-sub-Laplace operators. As applications of this result we obtain exact capacity estimates, representation formulas and an explicit sharp constant for the Moser-Trudinger inequality. We also obtain topological and measure-theoretic consequences for quasiregular mappings.