Hadamard type variation formulas for the eigenvalues of the $\eta$-Laplacian and applications

J. N. V. Gomes, M. A. M. Marrocos, R. R. Mesquita

We consider an analytic family of Riemannian metrics on a compact smooth manifold $M$. We assume the Dirichlet boundary condition for the $\eta$-Laplacian and obtain Hadamard type var…