OAI/Geometry/RCD/Metric/PointedCompactness.lean
1 declarations, 0 contain sorry, 0 declared as axioms
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.
- theorem
OAI.RegularPointCoordinates.NoncollapsedRCD.pointedRescalingPrecompactnessline 23Source 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