Convex model radial inverse maps tangent
ProvedBirkhoffGlobalSection.convex_model_radial_inverse_maps_tangentconvex-geometryreal-analysis
The derivative of the inverse radial chart sends model energy-tangent boundary vectors to sphere-tangent vectors.
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_radial_inverse_maps_tangent :
∀ {μ c : ℝ}
(M : ConvexRegularizationModel μ c) (y w : Phase) (hy : y ∈ frontier M.body)
(hw : fderiv ℝ M.modelHamiltonian y w = 0),
let u := radialNormalize y
let v := fderiv ℝ radialNormalize y w
u 0 * v 0 + u 1 * v 1 + u 2 * v 2 + u 3 * v 3 = 0 := by sorrySource
Independent extraction of component 11 of the Proved theorem BirkhoffGlobalSection.reverse_radial_variation_bundle. Original verified source: Solutions/Sol_BirkhoffGlobalSection_reverse_radial_variation_bundle.lean. Exact original component retained.