The Schwarz Lemma at the Boundary of the Non-Convex Complex Ellipsoids

Abstract

Let B2,p:= {z ∈ ℂ2: ∣z1∣2+ ∣z2∣p < 1} (0 < p< 1). Then, B2,p(0 < p < 1) is a non-convex complex ellipsoid in ℂ2 without smooth boundary. In this article, we establish a boundary Schwarz lemma at z0 ∈ ∂B2,p for holomorphic self-mappings of the non-convex complex ellipsoid B2, p, where z0 is any smooth boundary point of B2,p.