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Minimal surfaces and Schwarz lemma - MaRDI portal

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Minimal surfaces and Schwarz lemma

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Publication:6289834

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DOI10.1016/J.INDAG.2023.01.002arXiv1708.01848WikidataQ124879932 ScholiaQ124879932MaRDI QIDQ6289834

Author name not available (Why is that?)

Publication date: 6 August 2017

Abstract: We prove a sharp Schwarz type inequality for the Weierstrass- Enneper representation of the minimal surfaces. It states the following. If

F : m a t h b f D o S i g m a

is a conformal harmonic parameterization of a minimal disk

S i g m a

, where

m a t h b f D

is the unit disk and

| S i g m a | = p i R^{2}

, then

| F_{x} (z) | (1 - | z |^{2}) l e R

. If for some

z

the previous inequality is equality, then the surface is an affine disk, and

F

is linear up to a M"obius transformation of the unit disk.

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