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A simple proof is given for Nehari's theorem that an analytic function f which maps the unit disk onto a convex region has Schwarzian norm kSfk • 2. The inequality in sharper form leads to the conclusion that no convex mapping with kSfk = 2 can map onto a quasidisk. In particular, every bounded convex mapping has Schwarzian norm kSfk < 2. The analysis involves a structural formula for the pre-Schwarzian of a convex mapping, which is studied in further detail.

Schwarzian derivatives of convex mappings