Claims

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1961_01_01_pommerenke: Pommerenke's 1961 Theorem 14: for large p and a slightly above (1 + 1/p) p^{1/(p+1)}, the set where |z^p (z - a)| <= 1 has two components, one of them not convex, the negative answer to Grunsky's question; refereed.

1966_04_01_goodman: Goodman's 1966 counterexamples to Grunsky's question for the open sublevel set: (z^2 + 1)(z - 2)^2 and a quartic with four simple roots, each with a nonconvex component at a critical level; refereed.

2026_01_21_alexeev: A Lean 4 proof, found by Aristotle and published by Boris Alexeev, that the six roots of z^6 - z lie in six distinct components of the set where |z^6 - z| <= 0.582, and the one containing 0 is not convex.

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