The Schwarz lemma for holomorphic and minimal disks at the boundary

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.