Engle群上次Laplace算子的特征值不等式

INEQUALITIES FOR EIGENVALUES OF THE SUB-LAPLCAIN ON THE ENGEL GROUP

Engel群是次黎曼几何中的一类重要的单连通幂零李群.本文研究了Engel群E=(R^(4),■,{δλ})的有界区域Ω上次Laplace算子△_(E)的狄利克雷特征值问题■其中v是边界?Ω的单位外法向量场.我们建立了该问题的一些万有特征值不等式.

The Engel groups are one important kind of simply connected nilpotent Lie groups in sub-Riemannian geometry.In this paper,we investigate the Dirichlet eigenvalue problem of the sub-Laplacian Δ_(E) on a bounded domain Ω of the Engel group E=(R^(4),■,{δλ}) as follows■ where v is the outwards unit normal vector field of ?Ω.We establish some universal inequalities for eigenvalues of this problem.