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Univalent Bloch-Landau Constant

The univalent Bloch-Landau constant U is the infimum, over injective holomorphic functions f on the unit disk, of R_f/|f^'(0)|, where R_f is the supremum of the radii of disks contained in f(D). The disk centers may vary. Equivalently, the infimum may be taken over univalent functions normalized by f(0)=0 and f^'(0)=1 (Landau 1929).

Wikström (2026) obtained the analytic bound U>=0.592, an interval-certified bound U>=0.612242, and the upper bound U<0.6562681. Wikström (2026) reports AI assistance with mathematical analysis, certified computation, and Lean formalization. The formal analytic lower bound assumes the classical coefficient inequalities used in the argument.

See also

Bloch Constant, Landau Constant, Univalent Function

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References

Landau, E. "Über die Blochsche Konstante und zwei verwandte Weltkonstanten." Math. Z. 30, 608-634, 1929. https://doi.org/10.1007/BF01187791.Wikström, F. "Bounds for the Univalent Bloch-Landau Constant." 25 Oct 2026. https://arxiv.org/abs/2610.34580.

Cite this as:

Weisstein, Eric W. "Univalent Bloch-Landau Constant." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/UnivalentBloch-LandauConstant.html

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