Bloch constants and Bloch minimal surfaces
type: Item
instance of: scholarly article
title: Bloch constants and Bloch minimal surfaces
zbMATH Open document ID: 0658.53007
author: Shinji Yamashita
published in: Tokyo Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: A minimal surface x: D\(=\{| w| <1\}\to {\mathbb{R}}^ n\) is called Bloch if \(\sup_{w\in D}(1-| w|^ 2)| x_ u(w)| <\infty\). In the case \(n=2\) this is the Bloch condition of classical function theory. In the present paper the n-th Bloch constant \(b_ n\) is defined in terms of radii of certain disks on Bloch minimal surfaces. The inequality \(\sqrt{n}b_ n\geq b_ 2\) is proved with the classical Bloch constant \(b_ 2\).
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 30C55
zbMATH DE Number: 4075957
zbMATH Keywords: Bloch condition
zbMATH Keywords: Bloch constant
zbMATH Keywords: Bloch minimal surfaces
reviewed by: Fritz Gackstatter
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270134268
OpenAlex ID: W2086795216
DOI: 10.3836/TJM/1270134268
description: scientific article; zbMATH DE number 4075957