Heat flow of equivariant harmonic maps from \(\mathbb{B}^ 3\) into \(\mathbb{C}\mathbb{P}^ 2\)
type: Item
instance of: scholarly article
title: Heat flow of equivariant harmonic maps from \(\mathbb{B}^ 3\) into \(\mathbb{C}\mathbb{P}^ 2\)
zbMATH Open document ID: 0884.58034
published in: Pacific Journal of Mathematics
publication date: 1998-03-19T00:00:00Z
review text: The author investigates the existence of equivariant harmonic maps from the three-dimensional unit ball \(\mathbb{B}^3\) to the complex projective plane \(\mathbb{C}\mathbb{P}^2\), using the heat flow for the evolution equation of harmonic maps. The author shows that for certain equivariant initial and boundary conditions, there exists a global solution to this heat equation, which subconverges to an equivariant harmonic map with prescribed boundary as \(t\to\infty\). Here the images of the maps considered are not confined to some convex ball in \(\mathbb{C}\mathbb{P}^2\) but can reach any possible range.
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 1025795
zbMATH Keywords: harmonic maps
zbMATH Keywords: equivariant maps
zbMATH Keywords: equivariant boundary value problems
zbMATH Keywords: harmonic heat flow
author: Yuanlong Xin
reviewed by: Sebastian Goette
MaRDI profile type: Publication
full work available at URL: pjm.1996.176.563
OpenAlex ID: W1602337279
DOI: 10.2140/PJM.1996.176.563
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description: scientific article; zbMATH DE number 1025795