Update complexHarmonic.lean

This commit is contained in:
Stefan Kebekus 2024-05-15 21:17:42 +02:00
parent 1c34aee7be
commit bfeade4095
1 changed files with 9 additions and 12 deletions

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@ -159,6 +159,7 @@ theorem logabs_of_holomorphic_is_harmonic
have : (2 : )⁻¹ • (Real.log ∘ Complex.normSq ∘ f) = (fun z ↦ (2 : )⁻¹ • ((Real.log ∘ ⇑Complex.normSq ∘ f) z)) := by
simp
exact rfl
rw [this]
apply contDiff_iff_contDiffAt.2
@ -236,11 +237,11 @@ theorem logabs_of_holomorphic_is_harmonic
exact Complex.differentiableAt_log (h₃ z)
exact h₁ z
have : Complex.laplace (Complex.log ∘ f) = 0 := by
have t₁: Complex.laplace (Complex.log ∘ f) = 0 := by
let A := holomorphic_is_harmonic this
funext z
exact A.2 z
rw [this]
rw [t]
simp
have : Complex.log ∘ ⇑(starRingEnd ) ∘ f = ⇑(starRingEnd ) ∘ Complex.log ∘ f := by
@ -253,13 +254,9 @@ theorem logabs_of_holomorphic_is_harmonic
have : ⇑(starRingEnd ) ∘ Complex.log ∘ f = Complex.conjCLE ∘ Complex.log ∘ f := by
rfl
rw [this]
have : ContDiff 2 (Complex.log ∘ f) := by sorry
have : Complex.laplace (⇑Complex.conjCLE ∘ f) = ⇑Complex.conjCLE ∘ Complex.laplace (f) := by
sorry
sorry
rw [laplace_compCLE]
rw [t₁]
simp
sorry
sorry
sorry