Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold

Ahmad El Soufi, Saïd Ilias

For any bounded regular domain $\Omega$ of a real analytic Riemannian manifold $M$, we denote by ${\lambda }_k(\Omega )$ the $k$-th eigenvalue of the Dirichlet Laplacian of $\Omega$. In this paper, we co…