Let the $p$-component vector $X$ be normally distributed with mean $\xi$ and covariance $\sigma^2I$ where $I$ denotes the identity matrix and $\sigma$ is known. For estimating $\xi$ with quadratic loss, it is known that $X$ is minimax but inadmissible for $p \geqq 3$. We obtain a family of estimators which dominate $X$ and are admissible. These estimators are, therefore, both minimax and admissible.
"A Family of Admissible Minimax Estimators of the Mean of a Multivariate Normal Distribution." Ann. Statist. 1 (3) 517 - 525, May, 1973. https://doi.org/10.1214/aos/1176342417