Convex model contact variation path continuous
ProvedBirkhoffGlobalSection.convex_model_contact_variation_path_continuousconvex-geometryreal-analysis
For supplied continuous sphere-valued base and variational matrix curves, the convex model contact-coordinate action of each fixed initial plane vector is continuous in time.
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_contact_variation_preservation_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_contact_variation_path_continuous :
∀ {μ c : ℝ}
(M : ConvexRegularizationModel μ c) (q : ℝ → Phase)
(Z : ℝ → (Phase →L[ℝ] Phase)) (hs : ∀ t, q t ∈ unitThreeSphere)
(hq : Continuous q) (hZ : Continuous Z) (p : Plane),
Continuous (fun t => convexModelContactVariationPath M q Z t p) := by sorrySource
Independent extraction of component 10 of the Proved theorem BirkhoffGlobalSection.contact_variation_preservation_bundle. Original verified source: Solutions/Sol_BirkhoffGlobalSection_contact_variation_preservation_bundle.lean. Exact original component retained.