UniformCanonicalCenters.lean`

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One affine-center constant before all source centers and scales

theorem OAI.RegularPointCoordinates.canonical_dyadic_affine_centers_uniform line 17

Source documentation

A fixed upper bound on the splitting error makes the affine-center constant uniform in the root radius, center, sources, frames and map.

theorem canonical_dyadic_affine_centers_uniform {K : ℝ} (m : ℕ)
    (hX : NoncollapsedRCD K (m + 2) X) [IsFiniteMeasureOnCompacts (hausdorff (m + 2) X)]
    (hmean : LocalHarmonicL2MeanValueInput hX) {κ₀ deltaCap : ℝ}
    (hκ₀ : 0 ≤ κ₀) (_hcap : 0 ≤ deltaCap) :
    ∃ M : ℝ, 1 ≤ M ∧ ∀ {a κ r0 B J C L δ ε : ℝ} {p : X},
    0 ≤ a → 0 ≤ δ → δ ≤ deltaCap → ∀
    (_hBG : BallVolumeComparison (hausdorff (m + 2) X) (comparisonModelVolume (m + 1) a))
    (S : DyadicDistanceSources (hausdorff (m + 2) X) hX.quadratic (m + 2) κ p r0)
    (T : DyadicDistanceReplacements (hausdorff (m + 2) X) hX.quadratic S B J C)
    (u : Fin (m + 2) → SobolevSpace (hausdorff (m + 2) X) hX.quadratic)
    (v : X → Euclidean (m + 2))
    (_hu : FirstOrderSplittingOn (hausdorff (m + 2) X) hX.quadratic p r0 ε u v)
…

Mentions: OAI.RegularPointCoordinates.NoncollapsedRCD, OAI.RegularPointCoordinates.hausdorff, OAI.RegularPointCoordinates.LocalHarmonicL2MeanValueInput, OAI.RegularPointCoordinates.BallVolumeComparison, OAI.RegularPointCoordinates.comparisonModelVolume, OAI.RegularPointCoordinates.DyadicDistanceSources, OAI.RegularPointCoordinates.DyadicDistanceReplacements, OAI.RegularPointCoordinates.SobolevSpace, OAI.RegularPointCoordinates.Euclidean, OAI.RegularPointCoordinates.FirstOrderSplittingOn