Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 348-02. An L² Einstein Gap for Nonnegatively Curved Four-Manifolds
Manuscript map · lines 9105–9114
OpenAI@2026-10-07#rem:oai-p-348-02
Authors: OpenAI. Family 348.
Title: An L² Einstein Gap for Nonnegatively Curved Four-Manifolds.
Abstract: We prove a universal, scale-invariant L2 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 S4, ${}mathbb{CP}{}2$, 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 conclusion concerns the smooth manifold, not an isometry of the original metric.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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