The reduced Taylor polynomial of a composition equals the truncation of the composition of the reduced Taylor polynomials for C^k maps between Banach spaces.
Real and Functional Analysis , volume 142 of Graduate Texts in Mathematics
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An abstract perturbation theorem for Fredholm sections on compact zero sets that preserves existing transversality and supports cobordism arguments, shown via re-proof of Schwarz's theorem on Hamiltonian action functionals.
New elementary proofs establish complete Kobayashi hyperbolicity for the twice-punctured plane and bounded planar domains without using the disk cover or negative curvature, with applications to Picard-type theorems and a Hahn-inspired characterization.
A proof of the uniformization theorem for domains in the Riemann sphere is given via the Kobayashi metric without relying on the elliptic modular function.
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Fa\`a di Bruno is Taylor Composition
The reduced Taylor polynomial of a composition equals the truncation of the composition of the reduced Taylor polynomials for C^k maps between Banach spaces.