Laguerre minimal surfaces in \(\mathbb R^{3}\)
type: Item
instance of: scholarly article
title: Laguerre minimal surfaces in \(\mathbb R^{3}\)
zbMATH Open document ID: 1178.53065
author: Yu Ping Song
author: Changping Wang
publication date: 2009-01-05T00:00:00Z
review text: The authors relate generic Laguerre minimal surfaces to solutions of the Liouville equation, thus providing a way to obtain generic Laguerre minimal surfaces from holomorphic data. In the degenerate case, the authors relate Laguerre minimal surfaces to surfaces with vanishing mean curvature in a degenerate space. They prove that every Laguerre minimal surface with constant curvature of the induced metric of the ``mean curvature radii congruence'', an analogue of the central sphere congruence of Möbius geometry, is degenerate in the above sense, thus related to a zero mean curvature surface in a degenerate ambient geometry.
reviewed by: Udo Hertrich-Jeromin
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53A40
zbMATH DE Number: 5485332
zbMATH Keywords: Laguerre minimal surface
zbMATH Keywords: Liouville equation
zbMATH Keywords: Weierstrass representation
zbMATH Keywords: constant Gauss curvature
MaRDI profile type: Publication
full work available at URL: s10114-008-7117-0
OpenAlex ID: W2059128722
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DOI: 10.1007/S10114-008-7117-0
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5485332