Minimal immersions of surfaces by the first eigenfunctions and conformal area
type: Item
instance of: scholarly article
title: Minimal immersions of surfaces by the first eigenfunctions and conformal area
zbMATH Open document ID: 0584.53026
DOI: 10.1007/BF01388756
author: Antonio Ros
author: Sebastián Montiel
published in: Inventiones Mathematicae
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143307
review text: The authors study compact minimal surfaces immersed in a unit sphere for which 2 is the first eigenvalue of the Laplacian (or equivalently, the immersion is given by the first eigenfunctions). The main results are as follows: (1) For each conformal structure on a compact surface, there exists at most one metric which admits a minimal immersion into some unit sphere by the first eigenfunctions. (2) The only minimal torus immersed into \(S^ 3\) by the first eigenfunctions is the Clifford torus. (3) There exist conformal structures on a torus for which there are no metrics admitting minimal immersions into any sphere by the first eigenfunctions.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 3935902
zbMATH Keywords: minimal surfaces
zbMATH Keywords: Laplacian
zbMATH Keywords: conformal structure
zbMATH Keywords: first eigenfunctions
MaRDI profile type: Publication
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OpenAlex ID: W2139105139
description: scientific article; zbMATH DE number 3935902