Theorems · Theorem · complex analysis
Complex.eventually_eq_or_eq_zero_of_isLocalMin_norm
∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : E → ℂ} {c : E},
(∀ᶠ (z : E) in nhds c, DifferentiableAt ℂ f z) → IsLocalMin (norm ∘ f) c → (∀ᶠ (z : E) in nhds c, f z = f c) ∨ f c = 0- Defined in
- Mathlib.Analysis.Complex.AbsMax
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 292 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- nhdsstatement and proof · cited by 5,554
- Norm.normstatement and proof · cited by 5,413
- Filter.Eventuallystatement and proof · cited by 3,134
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- Filter.Eventually.monoproof · cited by 646
- DifferentiableAtstatement and proof · cited by 617
- Filter.Eventually.of_forallproof · cited by 526
Cited by1
Results whose statement or proof uses this declaration.
- DiffContOnCl.ball_subset_image_closedBallproof · cited by 1