Eigenvalue Problems of Hormander Operators on Non-equiregular sub-Riemannian Manifolds

目：Eigenvalue Problems of Hormander Operators on Non-equiregular sub-Riemannian Manifolds

: 2021623日上午1030

: 蒙明伟楼1105

要：We shall report some results on eigenvalue problems for degenerate elliptic operators, which including the results on closed eigenvalue problem and Dirichlet eigenvalue problem of self-adjoint Hörmander operators on non-equiregular sub-Riemannian manifolds. By Rayleigh-Ritz formula and the subelliptic heat kernel estimates ect., we establish the Weyl's asymptotic formula and the precise lower and upper bounds of eigenvalues which depend on the volume of subunit ball and the measure of the manifold. Under a certain condition, we obtain the explicit lower and upper bounds of eigenvalues which have the polynomially growth in k with the optimal order related to the non-isotropic dimension of the manifold.