Second Variation Formula for the Laplace Eigenvalue Functional on Closed Manifolds

Kazumasa Narita

For a closed Riemannian manifold $(M,g)$ of dimension $n$, let ${\lambda }_1(g)$ be the first positive eigenvalue of the Laplace--Beltrami operator ${\Delta }_g$ and $\mbox{Vol}(M,g)$ the volum…