The symmetric Mahler conjecture

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This event attributed to Unreleased internal OpenAI model

Lean: OAI/Analysis/Mahler/Classification.lean (symmetric_mahler_equality) evidence for this event

Vicente's question: is the Gromov width of every symmetric Lagrangian polar product equal to 4? evidence for this event

Theorem 1.1: for every $n\ge1$ and every origin-symmetric convex body $K\subset\mathbb R^n$, $|K|\,|K^\circ|\ge4^n/n!$, with equality iff $K$ is an invertible linear image of a Hanner polytope. The proof uses a planar conformal lens (a rotation of Gross's uniform-distribution map), a holomorphic mass estimate proved by Stokes' theorem, and, for equality, a metric-median property of the norm and Hansen-Lima's classification. The companion Symplectic Balls in Symmetric Polar Products gives an independent proof of the inequality (not of the equality cases) through the Gromov width of $\mathrm{int}\,K\times\mathrm{int}\,K^\circ$. It does not treat the non-symmetric problem (a separate entry) and gives no stability estimate. parent of this event

Mahler, Ein Ubertragungsprinzip fur konvexe Korper (1939) evidence for this event

Lean scope note for family 087 evidence for this event

Comparator statement SymmetricMahlerEquality.lean evidence for this event

Companion: The symmetric Mahler conjecture and its equality cases evidence for this event

Abridged reasoning summary released by OpenAI for family 087 evidence for this event

VibeMathed record: The symmetric Mahler conjecture evidence for this event

The symmetric Mahler conjecture parent of this event

Lean: OAI/Analysis/Mahler/MainTheorem.lean (symmetric_mahler) evidence for this event

The Mahler conjecture for general (non-symmetric) convex bodies evidence for this event

Comparator statement MahlerConjecture.lean evidence for this event