ScaledMeanPinching.lean`

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1 declarations, 0 contain sorry, 0 declared as axioms

The regular neighborhood with actual inverse mean-Gram mass matrices

theorem OAI.RegularPointCoordinates.exists_scaled_mean_pinching_neighborhood line 21
Source documentation
The precise published inputs construct one common harmonic/heat family with an arbitrarily small summable source and the full directional mass estimate for every nearby pair. No pinching hypothesis is assumed.
```
theorem exists_scaled_mean_pinching_neighborhood {K : ℝ} (m : ℕ)
    (hX : NoncollapsedRCD K (m + 2) X) [(hausdorff (m + 2) X).Regular]
    {p : X} {a : ℝ} (ha : 0 ≤ a)
    (hcompact : PointedRescalingPrecompactness p) (hregular : IsRegular (m + 2) p)
    (hvolume : EuclideanRescalingVolumeConvergence (hausdorff (m + 2) X) (m + 2) p
      (euclideanUnitVolume (m + 2)))
    (hmeasured : EuclideanMeasuredRescalingConvergence (hausdorff (m + 2) X) (m + 2) p)
    (hBG : BallVolumeComparison (hausdorff (m + 2) X) (comparisonModelVolume (m + 1) a))
    (hdensity : ∀ y, SmallScaleVolumeUpper (hausdorff (m + 2) X)
      (comparisonModelVolume (m + 1) a) y (euclideanUnitVolume (m + 2)))
    (hdistance : LocalSquaredDistanceInput hX) (hsobolev : LocalDirichletSobolevInput hX)
    (hpoisson : LocalPoissonGradientInput hX)
…
```
Mentions: OAI.RegularPointCoordinates.NoncollapsedRCD, OAI.RegularPointCoordinates.hausdorff, OAI.RegularPointCoordinates.PointedRescalingPrecompactness, OAI.RegularPointCoordinates.IsRegular, OAI.RegularPointCoordinates.EuclideanRescalingVolumeConvergence, OAI.RegularPointCoordinates.euclideanUnitVolume, OAI.RegularPointCoordinates.EuclideanMeasuredRescalingConvergence, OAI.RegularPointCoordinates.BallVolumeComparison, OAI.RegularPointCoordinates.comparisonModelVolume, OAI.RegularPointCoordinates.SmallScaleVolumeUpper, OAI.RegularPointCoordinates.LocalSquaredDistanceInput, OAI.RegularPointCoordinates.LocalDirichletSobolevInput, OAI.RegularPointCoordinates.LocalPoissonGradientInput