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This commit is contained in:
Stefan Kebekus 2024-04-28 21:17:45 +02:00
parent 90d3aceb95
commit ef75cb4579
3 changed files with 50 additions and 12 deletions
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17
nevanlinna/cauchyRiemann.lean
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@ -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.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.Basic
import Mathlib.Analysis.Calculus.FDeriv.RestrictScalars 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} variable {z : ℂ} {f : ℂ → ℂ}

39
nevanlinna/complexHarmonic.lean
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@ -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

6
nevanlinna/realHarmonic.lean
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@ -11,6 +11,6 @@ noncomputable def Real.laplace : (ℝ × ℝ → ℝ) → (ℝ × ℝ → ℝ) :
exact f₁₁ + f₂₂ exact f₁₁ + f₂₂
structure Harmonic (f : ℝ × ℝ → ℝ) : Prop where
ker_Laplace : ∀ x, Real.laplace f x = 0 def Harmonic (f : ℝ × ℝ → ℝ) : Prop :=
cont_Diff : ContDiff ℝ 2 f (ContDiff ℝ 2 f) ∧ (∀ x, Real.laplace f x = 0)