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arXiv · 2507.00819

The strong log-concavity for first eigenfunction of the Ornstein-Uhlenbeck operator in the class of convex bodies

Lei Qin
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Abstract

In this paper, we prove that the first (positive) Dirichlet eigenvalue of the Ornstein-Uhlenbeck operator \[ L(u)=\Delta u-(\nabla u,x), \] is strongly log-concave if the domain is bounded and convex, which improves the conclusion in [6]. We also provide a characterization of the equality case of the Brunn-Minkowski inequality for the principal frequency of $L(u)$ in the class of convex bodies.

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Lei Qin. 2025-07-01. The strong log-concavity for first eigenfunction of the Ornstein-Uhlenbeck operator in the class of convex bodies. https://arxiv.org/abs/2507.00819

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