Minimal surfaces and Schwarz lemma

被引：2

作者：

Kalaj, David ^{[1
]}

机构：

[1] Univ Montenegro, Fac Nat Sci & Math, Podgorica 81000, Montenegro

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2023年 / 34卷 / 03期

关键词：

Minimal surfaces; Schwarz lemma; Unit disk; INEQUALITY;

D O I：

10.1016/j.indag.2023.01.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a sharp Schwarz lemma type inequality for the Weierstrass-Enneper parameterization of minimal disks. It states the following. If F : D & RARR; & sigma; is a conformal harmonic parameterization of a minimal disk & sigma; & SUB; R3, where D is the unit disk and |& sigma;| = & pi; R2, then |Fx(z)|(1 - |z|2) & LE; R. If for some z the previous inequality is equality, then the surface is an affine image of a disk, and F is linear up to a Mobius transformation of the unit disk. & COPY; 2023 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

引用

页码：637 / 642

页数：6

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