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De Lellis--Topping almost-Schur inequality

Arthur Freitas Ramos, David Barros Hulak, Ruy J. G. B. de Queiroz

Palomar Registrypalomar/PALOMAR-2026-09-07-000015Sep 7, 2026math.DGscore 0

Formalizes the quantitative almost-Schur lemma on nonempty connected closed smooth Riemannian manifolds of dimension at least three with nonnegative Ricci curvature: scalar-curvature variance is bounded by 4*n*(n-1)/(n-2)^2 times the squared L2 norm of trace-free Ricci, with the Einstein equality characterization. The development constructs normalized Riemannian volume, solves the mean-zero Poisson problem variationally and upgrades it to a smooth representative, proves the actual integrated Bochner and contracted-Bianchi identities, and closes the sharp algebra.

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