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March 15, 2026Proceedings of the American Mathematical Society

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

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LQLei Qin

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Overview

Demonstrates strong log-concavity of the Dirichlet eigenvalue in convex bodies, implying improved insights into the Brunn-Minkowski inequality.

Key Points

  • To establish strong log-concavity for the first Dirichlet eigenvalue of the Ornstein-Uhlenbeck operator.
  • Prove the strong log-concavity under bounding convex domains.
  • Characterize equality conditions for the Brunn-Minkowski inequality.
  • The Dirichlet eigenvalue is shown to be strongly log-concave within convex bodies.
  • An improved conclusion over previous results by Colesanti et al. is noted.

Cite This Study

Lei Qin (2026) studied this question.

synapsesocial.com/papers/69b5ff8d83145bc643d1c64dhttps://doi.org/10.1090/proc/17590
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