OAI/Geometry/RCD/Transport/AsymmetricMidpoint.lean

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4 declarations, 0 contain sorry, 0 declared as axioms

Midpoint transport with separately controlled endpoint densities

The distance-Laplacian construction needs concentration of one endpoint at a pole. Equal endpoint bounds lose all control in that limit. Here the actual CD inequality retains the two inverse density powers separately.

  1. theorem OAI.RegularPointCoordinates.cd_midpoint_renyi_lower_asymmetric line 21
  2. theorem OAI.RegularPointCoordinates.FullCD.exists_midpoint_ac_support_bound_asymmetric line 63
  3. def OAI.RegularPointCoordinates.midpointSupportFactor line 102

    Source documentation

    The volume factor from the two separately bounded endpoint densities.

    noncomputable def midpointSupportFactor (K : ℝ) (n : ℕ) (D : ℝ)
        (C₀ C₁ : ℝ≥0∞) : ℝ≥0∞ :=
    …
  4. theorem OAI.RegularPointCoordinates.midpointSupportFactor_scale line 106