Author

S. Artstein-Avidan

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Preprint Sep 2026

A sharp Santal\'o inequality in a slab with centrally symmetric sections

We prove a sharp Santal\'o-type inequality for the product of $V(\varphi)$ and $V$ of the Legendre transform of $\varphi$, where $\varphi$ is an even geometric convex function on $\mathbb{R}^n$ and $V(\varphi)=\int(1+\varphi)^{-(n+1)}$. For this size functional, the Legendre transform and functional polarity give the s...

S. Artstein-Avidan · 0 citations

Preprint Sep 2026

Uncentered Blaschke-Santal\'o inequalities for the Gaussian measure

We study the maximizers of the generalized volume product \[ \gamma_\sigma^n(A)\,\gamma_\sigma^n(A^\circ) \] among all measurable subsets $A\subset\mathbb{R}^n$, where $A^\circ$ denotes the polar set of $A$, and where $\gamma_\sigma^n$ denotes the centered Gaussian probability measure on $\mathbb{R}^n$ with covariance...

S. Artstein-Avidan, M. Fradelizi, K. Wyczesany · 0 citations