The Schwarz lemma for holomorphic and minimal disks at the boundary

Summary · qwen2.5:32b

The article proves a Boundary Schwarz lemma for holomorphic disks on the unit ball in $\mathbb{C}^n$ and extends this to minimal conformal disks at the boundary using Forstnerič and Kalaj's work, establishing key results in complex analysis and differential geometry. This matters as it advances understanding of geometric properties of holomorphic and minimal disks. The proof utilizes a Schwarz lemma for harmonic maps which are conformal at a point from Forstnerič and Kalaj’s 2024 paper.

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Discussing the Schwarz lemma for holomorphic and minimal disks at the boundary in complex analysis.

Excerpt

arXiv:2509.09471v4 Announce Type: replace Abstract: We first prove a Boundary Schwarz lemma for holomorphic disks on the unit ball in $\mathbb{C}^n$. Further by using a Schwarz lemma for minimal conformal disks of Forstneri\v c and Kalaj (F.~Forstneri{\v{c}} and D.~Kalaj. \newblock Schwarz-pick lemma for harmonic maps which are conformal at a point. \newblock {\em Anal. PDE}, 17(3):981--1003, 2024.) we prove the boundary Schwarz lemma for such minimal disks.