New proofs are supplied for the Brunn-Minkowski inequality on Dirichlet eigenvalues and the log-concavity of the ground-state eigenfunction for Schrödinger operators on suitable domains.
A Brunn-Minkowski inequality for the Hessian eigenvalue in three-dimensional convex domain
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Convexity inequalities for eigenvalues and log-concavity of eigenfunctions
New proofs are supplied for the Brunn-Minkowski inequality on Dirichlet eigenvalues and the log-concavity of the ground-state eigenfunction for Schrödinger operators on suitable domains.