Open Research Index

GromovMilman

Arseniy Akopyan

Palomar Registrypalomar/PALOMAR-2026-10-18-000025Oct 18, 2026math.MGscore 0

Formalization of Theorem 1 (the Gromov–Milman conjecture on polynomials restricted to subspaces) from Dol'nikov–Karasev, "Dvoretzky type theorems for multivariate polynomials and sections of convex bodies" (arXiv:1009.0392): for any even d > 0 and any k, there exists n(d, k) such that every homogeneous polynomial of degree d on R^n (n >= n(d, k)) restricts on some k-dimensional subspace V to a scalar multiple of (x_1^2 + ... + x_n^2)^(d/2). The formalization provides an unconditional, constructive proof without sorry or external topological black boxes: Carlsson's theorem on non-abelian…

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