OAI/Analysis/AffineBernstein/ActualGlobalBase.lean

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1 declarations, 0 contain sorry, 0 declared as axioms

1. theorem OAI.AffineBernstein.affineEpigraph_global_base_identity line 22

   Source comment

   Compact product base IBP on the actual tube, rather than a formal drift identity.

   theorem affineEpigraph_global_base_identity {n : ℕ} {Ω : Set (Space n)}
       (hΩ : IsOpen Ω) (hcv : Convex ℝ Ω) {u : Space n → ℝ}
       (hu : ContDiffOn ℝ ∞ u Ω) (hp : ∀ x ∈ Ω, (hessian u x).PosDef)
       (a : Space n × ℝ) (L : (S × E) ≃L[ℝ] (Space n × ℝ))
       {D : Set S} (hD : IsOpen D)
       (hK : ∀ s ∈ D, IsCompact {y | (s,y) ∈ affineEpigraphPullback Ω u a L})
       (hzero : ∀ s ∈ D, (0 : E) ∈ interior {y | (s,y) ∈ affineEpigraphPullback Ω u a L})
       (bS : Module.Basis ι ℝ S) (bE : OrthonormalBasis (κ ⊕ Unit) ℝ E)
       {σ : S → ℝ} (hσ : ContDiff ℝ ∞ σ) (hc : HasCompactSupport σ) (hσD : tsupport σ ⊆ D)
       {g : S × E → ℝ} (hg : ∀ q ∈ tubeOpenSet D, ContDiffAt ℝ ∞ g q) :
       let H := fun q : S × E => homogeneousSupport {y | (q.1,y) ∈ affineEpigraphPullback Ω u a L} q.2
   …

   Mentions: OAI.AffineBernstein.Space, OAI.AffineBernstein.hessian, OAI.AffineBernstein.affineEpigraphPullback, OAI.AffineBernstein.tubeOpenSet, OAI.AffineBernstein.homogeneousSupport