Engel群的几个性质

Some properties on the Engel group

借助于Engel群上的基向量场给出了Engel群上光滑函数的泰勒展开式和群上乘法,并将粘性解定义和绝对最小者定义扩充到Engel群上,讨论了在粘性解意义下无限调和函数的存在惟一性,无限调和函数与绝对最小者的关系,得到了绝对最小者的惟一性.

Taylor expansion of smooth function on Engel group and the group product are obtained in virtue of the basis of Lie algebra of Engel group. The concepts of viscosity solution and absolute minimizers are extended to setting of Engel group. The existence-uniqueness of infinite harmonic functions in the viscosity sense and the relationship between absolute minimizers and infinite harmonic functions are discussed. As a consequence, the uniqueness of absolute minimizers is concluded.