Polynomial hulls and an optimization problem

摘要: We say that a subset of Cn is hypoconvex if its complement the union complex hyperplanes. it strictly smoothly bounded and at every point boundary real Hessian defining function positive definite on tangent space point. Let Bn be open unit ball in Cn.Suppose K C∞ compact manifold ∂B1 × Cn, n > 1, diffeomorphic to ∂Bn, each whose fibers Kz over bounds connected set. polynomialhull K. Then we show K∖K graphs analytic vector valued functions B1. This result shows an unnatural assumption regarding deformability earlier version this unnecessary. Next, study H∞ optimization problem. If pis real-valued ∂B1× infimum γρ = infƒ∈H ∞ (B1)n ‖ρ(z, ƒ (z))‖∞ attained by unique provided set (z, w) ∈ C n¦ρ(z, ≤ has circle.