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arXiv · 2509.21313

Some shape functionals for the $k$-Hessian equation

Alba Lia Masiello·Francesco Salerno
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Abstract

For a non-empty, bounded, open, and convex set of class $C^2$, we consider the Torsional Rigidity associated to the $k$-Hessian operator. We first prove P\'olya type lower bound for the $k$-Torsional Rigidity in any dimension; then, in order to investigate optimal sets in the P\'olya type inequality, we provide two quantitative estimates.

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Alba Lia Masiello, Francesco Salerno. 2025-09-25. Some shape functionals for the $k$-Hessian equation. https://arxiv.org/abs/2509.21313

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