Exact-Affine Rigidity for Log-Concave Measures and Structural Advances Toward the KLS Conjecture

Максим Вячеславович Чурилов

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Exact-Affine Rigidity for Log-Concave Measures and Structural Advances Toward the KLS Conjecture

М. В. Чурилов

2026-04-25

https://doi.org/10.24108/preprints-3115044

Let ν = e−W dz be a log-concave probability measure on a Euclidean space E with W ∈ C2(E) convex and Legendre-type, and let m = e−ϕ dy be log-concave on an interval I ⊂ R. We study the rigidity of exact-affine bundles T (z, y) = (A(y)z + b(y), y) whose pushforward T#(ν ⊗ m) is log-concave, and develop a systematic structural theory with applications toward the Kannan–Lovász–Simonovits (KLS) conjecture.

Ссылка для цитирования:

Чурилов М. В. 2026. Exact-Affine Rigidity for Log-Concave Measures and Structural Advances Toward the KLS Conjecture. PREPRINTS.RU. https://doi.org/10.24108/preprints-3115044

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