OAI/Geometry/RCD/Metric/PointedCompactness.lean

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Pointed precompactness of RCD rescalings

Uniform finite nets, a countable distance-matrix limit, and metric completion supply the precise pointed compactness input. The only tail restriction makes the rescaled curvature at least minus one.

  1. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.pointedRescalingPrecompactness line 23

    Source documentation

    The pointed rescaling compactness premise follows from the actual CD condition and completeness in the manuscript's dimension range.

    theorem NoncollapsedRCD.pointedRescalingPrecompactness {K : ℝ} {n : ℕ}
        (hX : NoncollapsedRCD K n X) (hn : 2 ≤ n) (p : X) :
        PointedRescalingPrecompactness p := by
    …

    Mentions: OAI.RegularPointCoordinates.NoncollapsedRCD, OAI.RegularPointCoordinates.PointedRescalingPrecompactness