Convex model frontier tangent curve
ProvedBirkhoffGlobalSection.convex_model_frontier_tangent_curveconvex-geometryreal-analysis
At a convex model boundary point, every vector in the Hamiltonian differential kernel is the velocity of a curve locally contained in the boundary.
All displayed regularity, tangency, normalization and supplied-data hypotheses of the exact formal statement are retained. This is a conditional result for the defined convex regularization model, not a global-section or index-existence theorem.
Preamble
import Theorems.Thm_BirkhoffGlobalSection_reverse_radial_variation_bundle open BirkhoffGlobalSection Set Filter SignType open scoped ContDiff Topology set_option linter.unusedVariables false set_option autoImplicit false set_option maxHeartbeats 800000
Formal statement
theorem BirkhoffGlobalSection.convex_model_frontier_tangent_curve :
∀ {μ c : ℝ}
(M : ConvexRegularizationModel μ c) (y w : Phase) (hy : y ∈ frontier M.body)
(hw : fderiv ℝ M.modelHamiltonian y w = 0),
∃ γ : ℝ → Phase, γ 0 = y ∧ HasDerivAt γ w 0 ∧
∀ᶠ s in 𝓝 0, γ s ∈ frontier M.body := by sorrySource
Independent extraction of component 5 of the Proved theorem BirkhoffGlobalSection.reverse_radial_variation_bundle. Original verified source: Solutions/Sol_BirkhoffGlobalSection_reverse_radial_variation_bundle.lean. Exact original component retained.