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Strict Log-Concavity of First Dirichlet Eigenfunctions under Symmetry in $\mathbb{CP}^n$
We prove that the positive first Dirichlet eigenfunction of every smooth domain with convex boundary in $\mathbb{CP}^n$ invariant under the standard $U(1)\times U(n-1)$-action is strictly log-concave for $n=2,3,4$.
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