The Schwarz lemma for holomorphic and minimal disks at the boundary
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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.
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Cited by 2 Pith papers
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Characterizes holomorphic mappings on B_ℓ_p^n × D^m and proves boundary Schwarz lemmas plus rigidity theorems for self-maps of ℓ_p balls in several complex variables.
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Improves Osserman and Chen et al. Schwarz lemmas in Banach spaces, derives sharp boundary versions for holomorphic maps and PDE solutions, and applies them to Minda inequalities and subball bounds.
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