Complex

Results named in Tau Ceti's TauCeti.Analysis.Complex modules and in no roadmap's section, as Tau Ceti has them at commit ace60277.

The angle condition of… to The Herglotz formula on a disc

• The angle condition of Poincaré's theorem
• The Apollonius identity for the Moebius factor
• The bounded-image form of the small-Jordan-curve theorem
• The Calderón–Zygmund inequality for the Cauchy–Riemann operator
• Carathéodory's theorem for the inside of a Jordan curve
• Cauchy estimate
• Cauchy-Laurent coefficient formula
• The Cauchy–Pompeiu formula for a compactly supported C¹ map u : ℂ → F
• Complex analytic Weierstrass division theorem
• Complex analytic Weierstrass preparation theorem
• The component mapping theorem from one boundary sheet
• The cusp condition of Poincaré's theorem
• The disc Schwarz--Christoffel theorem for an unbounded polygonal Jordan domain
• The discreteness part of Poincaré's polygon theorem
• The Dolbeault lemma on a disc
• The explicit Schwarz--Christoffel formula for a strip
• The fundamental-set part of Poincaré's polygon theorem
• Gauss–Bonnet for the triangles of the fan from ∞
• The Gauss–Bonnet formula
• The Herglotz formula on a disc

The Herglotz representation… to Schwarz's lemma with prescribed…

• The Herglotz representation theorem
• Identity theorem
• The identity theorem for Riemann surfaces
• Identity theorem on a right half-plane
• The infinitesimal Schwarz--Pick inequality
• Jensen's inequality from below
• The joint holomorphic implicit function theorem
• Laurent's theorem on an open concentric annulus
• Liouville's theorem for functions of negative order
• Montel's selection theorem
• Montel's theorem as an equivalence
• The Morse index bound λ ≤ n
• The open mapping theorem
• Phragmén–Lindelöf principle on the upper half-plane
• The Poisson lower bound of a Nevanlinna representation
• The presentation part of Poincaré's polygon theorem
• The Riemann extension theorem across a coordinate hyperplane
• Rigidity in the Schwarz--Pick theorem
• The Schoenflies theorem
• Schwarz's lemma with prescribed zeros

Schwarz–Pick, Lipschitz form to Weyl's lemma for \bar∂

• Schwarz–Pick, Lipschitz form
• Shimizu's inequality at two cusps
• The Stieltjes--Perron vanishing theorem
• Uniqueness in the Riemann mapping theorem, up to a disc automorphism
• Weyl's lemma for \bar∂

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