Bloch constants and Bloch minimal surfaces (Q1111163)

A minimal surface x: D\(=\{| w| <1\}\to {\mathbb{R}}^ n\) is called Bloch if \(\sup_{w\in D}(1-| w|^ 2)| x_ u(w)| <\infty\). In the case \(n=2\) this is the Bloch condition of classical function theory. In the present paper the n-th Bloch constant \(b_ n\) is defined in terms of radii of certain disks on Bloch minimal surfaces. The inequality \(\sqrt{n}b_ n\geq b_ 2\) is proved with the classical Bloch constant \(b_ 2\).