{"id":"openai-math/An-L2-Einstein-Gap-for-Nonnegatively-Curved-Four-Manifolds","pdf":"https://github.com/openai/math/blob/main/preprints/An-L2-Einstein-Gap-for-Nonnegatively-Curved-Four-Manifolds-October-5-2026/einstein-gap.pdf","url":"https://github.com/openai/math/tree/main/preprints/An-L2-Einstein-Gap-for-Nonnegatively-Curved-Four-Manifolds-October-5-2026","tags":["riemannian-geometry","curvature"],"score":0,"title":"An L² Einstein Gap for Nonnegatively Curved Four-Manifolds","domain":"Differential geometry","family":"348","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"We prove a universal, scale-invariant L 2 gap for the trace-free Ricci tensor on simply connected closed four-manifolds with nonnegative sectional curvature. If the trace-free Ricci energy is sufficiently small, the manifold is diffeomorphic to S 4 , $`\\mathbb{CP}^2`$, or $`S^2\\times S^2`$. The proof uses the classification of positive-Einstein, nonnegatively curved four-manifolds supplied by the companion zero-plane rigidity theorem, stated explicitly as the classification premise of our result. No auxiliary curvature, volume, diameter, injectivity-radius, or Sobolev bound is required. The…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Nonnegative-curvature Einstein classification and an L 2 topological gap"}