The first eigenvalue of p-Laplacian and geometric estimates
The first eigenvalue of p-Laplacian and geometric estimates
We investigate the nonlinear eigenvalue problem for the p-Laplacian on compact manifold with zero boundary condition.In particular, we obtain classical estimates of Faber-Krahn inequality and Cheeger-type inequality for the first eigenvalue.As an application we derive Mckeantype estimate and discuss some geometric estimates involving the L p -Sobolev constants.