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Let $(M^{n}, g)$ be a closed connected Einstein space, $n=dim M ,$ and$\kappa_{0} $ be the lower bound of the sectional curvature. In this paper, weprove Udo Simon conjecture: on closed Einstein spaces, $n\geq 3,$ there is noeigenvalue $\lambda$ such that $$n\kappa_{0} < \lambda < 2(n + 1)\kappa_{0},$$and both bounds are the best possible.

Curvature bounds for the spectrum of closed Einstein spaces and Simon conjecture