Let $M$ be a complete Riemannian manifold. Denote $\Delta_M\ge0$ the unique self-adjoint extension of the Laplace-Beltrami operator in $L^2(M)$ and $\sigma(\Delta_M)\subset [0,\infty)$ its spectrum. Further define:

$$\lambda(M):=\inf\{\mu\in\sigma(\Delta_M)\vert~\mu\neq 0\}$$
**Question:** Let $N$ be a complete Riemannian manifold with $\lambda(N)>0$. If $p\colon \hat N\rightarrow N$ is a finite sheeted Riemannian covering, do we also have $\lambda(\hat N)>0$?

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