SOME PROPERTIES OF H¨ OLDER SURFACES IN THE HEISENBERG GROUP
SOME PROPERTIES OF H¨ OLDER SURFACES IN THE HEISENBERG GROUP
复制标题
海森堡群中支架表面的一些性质
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
R. Zust
中科院分区：
文献类型：
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作者：
E. Donne;R. Zust
一个民间猜想是，对于�>；1/2，在次黎曼海森堡群中不存在�-Holder曲面。也就是说，不存在从R2的开子集到严格大于1/2阶的Holder连续的Heisenberg群的嵌入。这里的Heisenberg群有它的Carnot-Caratheodory距离。我们证明了，在这样的曲面存在的情况下，它不可能是本质有界变差的，并且它至少与拓扑Cantor集中的某条垂直线相交。
It is a folk conjecture that for � > 1/2 there is no �-Holder surface in the subRiemannian Heisenberg group. Namely, it is expected that there is no embedding from an open subset of R 2 into the Heisenberg group that is Holder continuous of order strictly greater than 1/2. The Heisenberg group here is equipped with its Carnot-Caratheodory distance. We show that, in the case that such a surface exists, it cannot be of essential bounded variation and it intersects some vertical line in at least a topological Cantor set.