The first Dirichlet eigenfunction of the Ornstein-Uhlenbeck operator on any bounded convex domain is strongly log-concave, and the equality case in the Brunn-Minkowski inequality for its principal frequency is characterized up to translation.
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The strong log-concavity for first eigenfunction of the Ornstein-Uhlenbeck operator in the class of convex bodies
The first Dirichlet eigenfunction of the Ornstein-Uhlenbeck operator on any bounded convex domain is strongly log-concave, and the equality case in the Brunn-Minkowski inequality for its principal frequency is characterized up to translation.