diff --git a/nevanlinna/cauchyRiemann.lean b/nevanlinna/cauchyRiemann.lean index 5d649ed..db56f16 100644 --- a/nevanlinna/cauchyRiemann.lean +++ b/nevanlinna/cauchyRiemann.lean @@ -1,15 +1,14 @@ -import Mathlib.Analysis.Complex.CauchyIntegral -import Mathlib.Analysis.Complex.Basic -import Mathlib.Analysis.Calculus.LineDeriv.Basic -import Mathlib.Analysis.Calculus.ContDiff.Defs -import Mathlib.Analysis.Calculus.FDeriv.Basic -import Mathlib.Analysis.Complex.RealDeriv -import Mathlib.Analysis.Calculus.ContDiff.Basic -import Mathlib.Analysis.Calculus.Deriv.Linear -import Mathlib.Analysis.Complex.Conformal import Mathlib.Analysis.Calculus.Conformal.NormedSpace +import Mathlib.Analysis.Calculus.ContDiff.Basic +import Mathlib.Analysis.Calculus.ContDiff.Defs +import Mathlib.Analysis.Calculus.Deriv.Linear import Mathlib.Analysis.Calculus.FDeriv.Basic import Mathlib.Analysis.Calculus.FDeriv.RestrictScalars +import Mathlib.Analysis.Calculus.LineDeriv.Basic +import Mathlib.Analysis.Complex.Basic +import Mathlib.Analysis.Complex.CauchyIntegral +import Mathlib.Analysis.Complex.Conformal +import Mathlib.Analysis.Complex.RealDeriv variable {z : ℂ} {f : ℂ → ℂ} diff --git a/nevanlinna/complexHarmonic.lean b/nevanlinna/complexHarmonic.lean index e69de29..4318c6d 100644 --- a/nevanlinna/complexHarmonic.lean +++ b/nevanlinna/complexHarmonic.lean @@ -0,0 +1,39 @@ +import Mathlib.Analysis.Complex.Basic +import Mathlib.Analysis.Calculus.LineDeriv.Basic +import Mathlib.Analysis.Calculus.ContDiff.Defs +import Mathlib.Analysis.Calculus.FDeriv.Basic + +noncomputable def Real.laplace : (ℝ × ℝ → ℝ) → (ℝ × ℝ → ℝ) := by + intro f + let f₁ := fun x ↦ lineDeriv ℝ f x ⟨1,0⟩ + let f₁₁ := fun x ↦ lineDeriv ℝ f₁ x ⟨1,0⟩ + let f₂ := fun x ↦ lineDeriv ℝ f x ⟨0,1⟩ + let f₂₂ := fun x ↦ lineDeriv ℝ f₂ x ⟨0,1⟩ + exact f₁₁ + f₂₂ + +noncomputable def Complex.laplace : (ℂ → ℝ) → (ℂ → ℝ) := by + intro f + let f₁ := fun x ↦ lineDeriv ℝ f x 1 + let f₁₁ := fun x ↦ lineDeriv ℝ f₁ x 1 + let f₂ := fun x ↦ lineDeriv ℝ f x Complex.I + let f₂₂ := fun x ↦ lineDeriv ℝ f₂ x Complex.I + exact f₁₁ + f₂₂ + + +theorem xx : ∀ f : ℂ → , f = 0 := by + intro f + + let f₁ := fun x ↦ lineDeriv ℝ f x 1 + let f₂ := fun x ↦ lineDeriv ℝ f x Complex.I + + have : ∀ z, fderiv ℂ f z = 0 := by + sorry + + + have : (fun x ↦ lineDeriv ℝ f x 1) = (fun x ↦ lineDeriv ℝ f x Complex.I) := by + + unfold lineDeriv + + sorry + + sorry diff --git a/nevanlinna/realHarmonic.lean b/nevanlinna/realHarmonic.lean index b7889ae..92db0ab 100644 --- a/nevanlinna/realHarmonic.lean +++ b/nevanlinna/realHarmonic.lean @@ -11,6 +11,6 @@ noncomputable def Real.laplace : (ℝ × ℝ → ℝ) → (ℝ × ℝ → ℝ) : exact f₁₁ + f₂₂ -structure Harmonic (f : ℝ × ℝ → ℝ) : Prop where - ker_Laplace : ∀ x, Real.laplace f x = 0 - cont_Diff : ContDiff ℝ 2 f + +def Harmonic (f : ℝ × ℝ → ℝ) : Prop := + (ContDiff ℝ 2 f) ∧ (∀ x, Real.laplace f x = 0)