Universal inequalities for eigenvalues of a class of operators on Riemannian manifold (Q2403185)

Consider the eigenvalue problem \[ \Delta^2u=\lambda u\text{ and }u|_{\partial\Omega}=\partial_\nu u|_{\partial\Omega}=0. \] The authors use the Rayleigh-Ritz inequality to obtain universal inequalities for the eigenvalues in several contexts. One context is when \(\mathcal{M}\) is isometrically immersed in a Euclidean space. Other contexts include Hadamard manifolds with Ricci curvature bounded from below, a class of warped product manifolds, the product of Euclidean spaces with any complete manifold, and manifolds admitting eigenmaps to a sphere.