Q-valued functions revisited
Q-valued functions revisited
复制标题
重温 Q 值函数
DOI：
10.1090/s0065-9266-10-00607-1
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
E. Spadaro
中科院分区：
文献类型：
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作者：
Camillo De Lellis;E. Spadaro
在这篇笔记中，我们重温了Almgren的Q值函数理论，即在R^n中的无序Q-点元组空间中取值的函数。特别是：1）我们给出了Dir-minimizing Q-值函数存在性、Hoelder正则性和奇异集维数估计的Almgren证明的简化版本; 2）我们提出了一种替代的内在方法来证明这些结果，而不依赖于Almgren的biLipschitz嵌入; 3）改进了平面Dir-minimizing函数奇异集的估计，证明了它由孤立点组成。
In this note we revisit Almgren's theory of Q-valued functions, that are functions taking values in the space of unordered Q-tuples of points in R^n. In particular: 1) we give shorter versions of Almgren's proofs of the existence of Dir-minimizing Q-valued functions, of their Hoelder regularity and of the dimension estimate of their singular set; 2) we propose an alternative intrinsic approach to these results, not relying on Almgren's biLipschitz embedding; 3) we improve upon the estimate of the singular set of planar Dir-minimizing functions by showing that it consists of isolated points.