ABSTRACT
Gabriel’s Problem If Λ is a closed convex curve lying inside the closed convex curve Γ and if f is analytic inside Γ then:∫
|f(z)| | dz| < A ∫ Γ
|f(z)| | dz|,
where A is some absolute constant.
Comment Gabriel conjectured that A = 2 but while this is correct when Γ is a circle it is not true in general; the best known value is A = 3.6.
