On the eigenvalue counting function for weighted Laplace-Beltrami operators
It is well known that a weighted Laplace Beltrami operator on a Riemannian manifold \( M \) is an operator of the form: \[ H = - \overline{\sigma} ^2 \nabla (\sigma \nabla), \] where \( \sigma \) is a positive, locally bounded function defined on \( M \). In the paper under review the author obtains some upper and lower bounds on the eigenvalue counting function of \( H \) for a class of incomplete manifolds with locally bounded geometry and for certain weights \( \sigma \).
scientific article; zbMATH DE number 1542076
scientific article