Theorems · Theorem · global analysis

exists_isMIntegralCurveAt_of_contMDiffAt

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {H : Type u_2} [inst_2 : TopologicalSpace H]
  {I : ModelWithCorners ℝ E H} {M : Type u_3} [inst_3 : TopologicalSpace M] [inst_4 : ChartedSpace H M]
  [inst_5 : IsManifold I 1 M] {v : (x : M) → TangentSpace I x} (t₀ : ℝ) {x₀ : M} [CompleteSpace E],
  ContMDiffAt I I.tangent 1 (fun x => ⟨x, v x⟩) x₀ → I.IsInteriorPoint x₀ → ∃ γ, γ t₀ = x₀ ∧ IsMIntegralCurveAt γ v t₀

Existence of local integral curves for a $C^1$ vector field at interior points of a C^1 manifold.

Defined in

Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique

Cited by

1 results in Mathlib

Foundations

Depth 280 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceIsManifoldCompleteSpace