AI 中文总结
研究亚交换李群上秩2极化的异常集维数界及相关萨德性质，通过给出维数界确立终点映射萨德性质，还得到特定亚交换李群戈赫异常集维数界，推断相关极化群满足极小化萨德性质。
AI 中文摘要
我们给出了亚交换李群上秩2极化的异常集维数的界，确立了此类群终点映射的萨德性质。对于导子群余维数至多为2的亚交换李群，在不对极化秩作假设的情况下，我们也得到了戈赫异常集维数的界。由此推断，配备次黎曼结构的这些极化群满足极小化萨德性质。
英文摘要
We provide sharp bounds on the dimension of the abnormal set for rank $2$ polarizations on metabelian Lie groups, establishing the Sard property for the end-point map of such groups. The proof is based on a novel approach that makes essential use of tools from tame geometry. We also obtain bounds for the dimension of the Goh-abnormal set for metabelian Lie groups where the codimension of the derived subgroup is at most $2$, with no assumption on the rank of the polarization. We thus infer that these polarized groups, equipped with sub-Riemannian structures, satisfy the minimizing Sard property.
Comments22 pages
