The second variation of area of minimal surfaces in four-manifolds
type: Item
instance of: scholarly article
title: The second variation of area of minimal surfaces in four-manifolds
zbMATH Open document ID: 0788.58016
DOI: 10.1007/BF01444887
author: Mario J. Micallef
author: Jon G. Wolfson
published in: Mathematische Annalen
publication date: 1994-05-31T00:00:00Z
full work available at URL: https://eudml.org/doc/165042
review text: We study the second variation of area of an oriented minimal surface in an oriented Riemannian 4-manifold \(N\) whose curvature operator satisfies \({1 \over 6} S-W_ + \geq 0\) where \(S\) is the scalar curvature and \(W_ + :\Lambda^ 2_ + \to \Lambda^ 2_ +\) is the part of the Weyl curvature operator which maps self-dual two-forms \((\Lambda^ 2_ +)\) into themselves. Special attention is given to the case when \(N\) is Kähler and sharp results are obtained when \(N\) is hyper-Kähler. In particular, the relation between stability, holomorphicity and the complex and anti-complex tangent points of the minimal surface is investigated.
Mathematics Subject Classification ID: 58E12
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 537252
zbMATH Keywords: second variation of area
zbMATH Keywords: minimal surface
zbMATH Keywords: hyper-Kähler
zbMATH Keywords: stability
zbMATH Keywords: holomorphicity
zbMATH Keywords: tangent points
zbMATH Keywords: index
MaRDI profile type: Publication
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OpenAlex ID: W2087192538
description: scientific article; zbMATH DE number 537252