• Commutator Bounds for Eigenvalues, with Applications to Spectral Geometry 

      Harrell, Evans M., II; Michel, Patricia L. (Georgia Institute of Technology, 1994-03)
      We prove a purely algebraic version of an eigenvalue inequality of Hile and Protter, and derive corollaries bounding differences of eigenvalues of Laplace-Beltrami operators on manifolds. We significantly improve earlier ...
    • On the Second Eigenvalue of the Laplace Operator Penalized by Curvature 

      Harrell, Evans M., II (Georgia Institute of Technology, 1994)
      Consider the operator - ∇^2 - q(κ), where - ∇^2 is the (positive) Laplace-Beltrami operator on a closed manifold of the topological type of the two-sphere S^2 and q is a symmetric non-negative quadratic form in the principal ...