Conformal upper bounds for the eigenvalues of the p‐Laplacian

In this note we present upper bounds for the variational eigenvalues of $p$-Laplacian on smooth domains complete $n$-dimensional Riemannian manifolds and Neumann boundary conditions, compact (boundaryless) manifolds. particular, provide in conformal class a given manifold $(M,g)$ $11$ when fix metric $g$. To do so, use approach construction suitable test functions characterization eigenvalues. The agree with well-known asymptotic estimate due to Friedlander. We also hypersurfaces bounding terms isoperimetric ratio.