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arXiv · 2409.20269

The $L_{p}$-Brunn-Minkowski inequalities for variational functionals with $0\leq p<1$

Jinrong Hu
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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 $p \geq 0$. These formulations yield Poincar\'{e}-type inequalities related to these functionals. As an application, the $L_{p}$-Brunn-Minkowski inequalities for torsional rigidity with $0 \leq p < 1$ are confirmed for small $C^{2}$-perturbations of the unit ball.

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Jinrong Hu. 2024-09-30. The $L_{p}$-Brunn-Minkowski inequalities for variational functionals with $0\leq p<1$. https://arxiv.org/abs/2409.20269

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