The Schwarz lemma at the boundary of the non-convex complex ellipsoids. (English) Zbl 1499.32027
Summary: Let \(B_{2, p} := \{z\in\mathbb{C}^2: |z_1|^2+ |z_2|^p < 1\}\) (\(0 < p< 1\)). Then, \(B_{2, p}\) (\(0 < p < 1\)) is a non-convex complex ellipsoid in \(\mathbb{C}^2\) without smooth boundary. In this article, we establish a boundary Schwarz lemma at \(z_0 \in \partial B_{2, p}\) for holomorphic self-mappings of the non-convex complex ellipsoid \(B_{2, p}\), where \(z_0\) is any smooth boundary point of \(B_{2, p}\).
MSC:
| 32F45 | Invariant metrics and pseudodistances in several complex variables |
| 32H02 | Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables |
| 30C80 | Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination |
Keywords:
boundary Schwarz lemma; holomorphic mappings; Kobayashi metric; non-convex complex ellipsoidsReferences:
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