OAI/Geometry/RCD/Sobolev/PoissonActionFromScalar.lean

GitHub source file

2 declarations, 0 contain sorry, 0 declared as axioms

The exact mixed-action input from scalar dimensional Bochner

The same full measure appears in the local source identity, shifted positivity and every mixed-action estimate. Separate direction caps are retained, as required by the coordinate commutator.

  1. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.poisson_shifted_action_data_of_scalar line 22
  2. theorem OAI.RegularPointCoordinates.NoncollapsedRCD.poisson_hessian_action_input_of_scalar line 126

    Source documentation

    Scalar weak Bakry--Émery gives the local Hessian action bound.

    theorem NoncollapsedRCD.poisson_hessian_action_input_of_scalar {K : ℝ} {n : ℕ}
    (hX : NoncollapsedRCD K n X) [(hausdorff n X).Regular] (hn : 2≤n)
    (hscalar : ScalarDimensionalBochner (hausdorff n X) hX.quadratic K n) :
    LocalPoissonHessianActionInput hX := by
…

    Mentions: OAI.RegularPointCoordinates.NoncollapsedRCD, OAI.RegularPointCoordinates.hausdorff, OAI.RegularPointCoordinates.ScalarDimensionalBochner, OAI.RegularPointCoordinates.LocalPoissonHessianActionInput