In this paper, we are concerned with the Riesz means of Dirichlet eigenvalues for the sub-Laplace operator on the Engel group and deriver different inequalities for Riesz means. The Weyl-type estimates for means of ei...In this paper, we are concerned with the Riesz means of Dirichlet eigenvalues for the sub-Laplace operator on the Engel group and deriver different inequalities for Riesz means. The Weyl-type estimates for means of eigenvalues are given.展开更多
Let E be the Engel group and D be a bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, the author constructs a parametrization of a quas...Let E be the Engel group and D be a bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, the author constructs a parametrization of a quasi-pendulum equation by Jacobi functions, and then gets the space-like Hamiltonian geodesics in the Engel group with a sub-Lorentzian metric.展开更多
We show that conformal mappings between the Engel groups are CR or anti-CR mappings. This reduces the determination of conformal mappings to a problem in the theory of several complex analysis.The result about the gro...We show that conformal mappings between the Engel groups are CR or anti-CR mappings. This reduces the determination of conformal mappings to a problem in the theory of several complex analysis.The result about the group of CR automorphisms is used to determine the identity component of the group of conformal mappings on the Engel group.展开更多
文摘In this paper, we are concerned with the Riesz means of Dirichlet eigenvalues for the sub-Laplace operator on the Engel group and deriver different inequalities for Riesz means. The Weyl-type estimates for means of eigenvalues are given.
基金supported by the Science and Technology Development Fund of Nanjing Medical University(No.2017NJMU005).
文摘Let E be the Engel group and D be a bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, the author constructs a parametrization of a quasi-pendulum equation by Jacobi functions, and then gets the space-like Hamiltonian geodesics in the Engel group with a sub-Lorentzian metric.
基金supported by National Natural Science Foundation of China(Grant No.10871172)
文摘We show that conformal mappings between the Engel groups are CR or anti-CR mappings. This reduces the determination of conformal mappings to a problem in the theory of several complex analysis.The result about the group of CR automorphisms is used to determine the identity component of the group of conformal mappings on the Engel group.
