On eigenfunctions and nodal sets of the Witten-Laplacian

Source abstract

In this paper, we successfully establish a Courant-type nodal domain theorem for both the Dirichlet eigenvalue problem and the closed eigenvalue problem of the Witten-Laplacian. Moreover, we also characterize the properties of the nodal lines of the eigenfunctions of the Witten-Laplacian on smooth Riemannian 2-manifolds. Besides, for a Riemann surface with genus g, an upper bound for the multiplicity of closed eigenvalues of the Witten-Laplacian can be provided.