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  1. ; ; (, International Mathematics Research Notices)
    Abstract Suppose that $$\Sigma ^{n}\subset \mathbb{S}^{n+1}$$ is a closed embedded minimal hypersurface. We prove that the first non-zero eigenvalue $$\lambda _{1}$$ of the induced Laplace–Beltrami operator on $$\Sigma $$ satisfies $$\lambda _{1} \geq \frac{n}{2}+ a_{n}(\Lambda ^{6} + b_{n})^{-1}$$, where $$a_{n}$$ and $$b_{n}$$ are explicit dimensional constants and $$\Lambda $$ is an upper bound for the length of the second fundamental form of $$\Sigma $$. This provides the first explicitly computable improvement on Choi and Wang’s lower bound $$\lambda _{1} \geq \frac{n}{2}$$ without any further assumptions on $$\Sigma $$. 
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