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We discuss an eigenvalue estimate that holds on every embedded self-similar shrinker for mean curvature flow. This result is obtained via a Reilly-type formula and can be viewed as an analogue of the first eigenvalue estimate obtained by Choi and Wang for embedded minimal hypersurfaces in the round sphere. Our estimate generalizes earlier work of Ding and Xin on closed self-shrinkers by introducing and minimizing a new functional to treat the non-compact case. This is joint work with Simon Brendle.