An affirmative solution to the generalized Busemann-Petty problem with subspaces dimensions 2 and 3

Organisé par

Institut Henri Poincaré

The generalized Busemann--Petty problem asks whether two origin-symmetric convex bodies in $\mathbb{R}^n$ having larger volume of all $m$-dimensional sections necessarily have larger volume. When $m\geq 4$, this is known to be false, but the cases $m=2, 3$ for $n\geq 5$ have remained open since the 1990s. In this work, we resolve these cases. Together with the known results, the generalized Busema

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