Convex model contact coordinates continuous
ProvedBirkhoffGlobalSection.convex_model_contact_coordinates_continuousconvex-geometryreal-analysis
Along continuous sphere-valued base curves and continuous vector curves, convex model contact coordinates vary continuously.
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_coordinates_continuous :
∀ {μ c : ℝ}
(M : ConvexRegularizationModel μ c) (q v : ℝ → Phase)
(hq : Continuous q) (hv : Continuous v) (hs : ∀ t, q t ∈ unitThreeSphere),
Continuous (fun t => convexModelContactCoordinates M (q t) (v t)) := by sorrySource
Independent extraction of component 7 of the Proved theorem BirkhoffGlobalSection.contact_variation_preservation_bundle. Original verified source: Solutions/Sol_BirkhoffGlobalSection_contact_variation_preservation_bundle.lean. Exact original component retained.