The Schwarz lemma for holomorphic and minimal disks at the boundary
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917531892056064 |
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| author | Kalaj, David |
| author_facet | Kalaj, David |
| contents | 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{č} 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09471 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Schwarz lemma for holomorphic and minimal disks at the boundary Kalaj, David Complex Variables 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{č} 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. |
| title | The Schwarz lemma for holomorphic and minimal disks at the boundary |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2509.09471 |