The L_p-Brunn-Minkowski inequalities for variational functionals with 0≤ p<1

2024/09/30 by Jinrong Hu, Hu, Jinrong · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2409.20269

openalex publication_date 2024/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The infinitesimal forms of the L_p-Brunn-Minkowski inequalities for variational functionals, such as the q-capacity, the torsional rigidity, and the first eigenvalue of the Laplace operator, are investigated for p ≥ 0. These formulations yield Poincaré-type inequalities related to these functionals. As an application, the L_p-Brunn-Minkowski inequalities for torsional rigidity with 0 ≤ p &lt; 1 are confirmed for small C²-perturbations of the unit ball.

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