A quantitative result for the k-Hessian equation.

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• Alba Lia Masiello (Istituto Nazionale di Alta Matematica, Rome)
• Thursday 05 February 2026, 16:20-16:35
• Seminar Room 1, Newton Institute.

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GSTW05 - Emerging Horizons in Geometric Spectral Theory: an ECRs workshop

We consider a symmetrization procedure for convex function in $\mathbb{R}^n$ that preserves mixed volumes of the sublevel sets, and for which a Pólya-Szegő type inequality holds. We will obtain a stability improvement for this Pólya-Szegő type inequality,bounding the Pólya-Szegő deficit in terms of the Hausdor asymmetry index. This result allows us to prove a quantitative version of the Faber-Krahn and Saint-Venant inequalities for the k-Hessian equation, at least in the case when the aforementioned inequalities hold.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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