论文标题
步骤2和丝状carnot组中的sard问题
The Sard problem in step 2 and in filiform Carnot groups
论文作者
论文摘要
我们研究了一些著名的Carnot组中的端点图的SARD问题。我们的第一个主要结果涉及步骤2 Carnot组，在该组中，我们提供了下限（仅取决于该组的代数），以异常集合的编成。事实证明，我们的界限始终是至少3个，这改善了在ARXIV中证明的结果：1503.03610并解决了Arxiv中出现的问题：1709.02854。在我们的第二个主要结果中，我们表征了丝状组中的异常集，并表明它是水平线，或者是3维代数品种。
We study the Sard problem for the endpoint map in some well-known classes of Carnot groups. Our first main result deals with step 2 Carnot groups, where we provide lower bounds (depending only on the algebra of the group) on the codimension of the abnormal set; it turns out that our bound is always at least 3, which improves the result proved in arXiv:1503.03610 and settles a question emerged in arXiv:1709.02854. In our second main result we characterize the abnormal set in filiform groups and show that it is either a horizontal line, or a 3-dimensional algebraic variety.
