科研之友
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摘要
It is a folk conjecture that for alpha %26gt; 1/2 there is no alpha-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.
- 出版日期2013
