Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold
Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold
For any bounded regular domain $Ω$ of a real analytic Riemannian manifold $M$, we denote by $λ_{k}(Ω)$ the $k$-th eigenvalue of the Dirichlet Laplacian of $Ω$. In this paper, we consider $λ_k$ and as a functional upon the set of domains of fixed volume in $M$. We introduce and investigate …