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math.MG2026
Optimal bounds for convex bodies
Pierre Bizeul
Let be a convex body in isotropic position. We prove the optimal mean-width estimate \[ M^*(K)\leq C\sqrt{n\log n}. \] The main new ingredient is a geometric inequal…
math.MG2026
Distances between non-symmetric convex bodies: optimal bounds up to polylog
Pierre Bizeul, Boaz Klartag
In this paper we determine, up to polylogarithmic factors, the diameter of the Banach--Mazur compactum of -dimensional convex bodies without symmetry assumptions. We prove that…