The equator map and the negative exponential functional
type: Item
instance of: scholarly article
title: The equator map and the negative exponential functional
zbMATH Open document ID: 0768.58012
DOI: 10.1007/BF02567071
author: Min-Chun Hong
published in: Manuscripta Mathematica
publication date: 1993-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/155710
review text: The study of stability properties of the equator map \(u^*: B^ n \to S^ n\), \(n \geq 3\), provided insight into the regularity theory of harmonic maps between Riemannian manifolds (here \(B^ n\) denotes the Euclidean unit \(n\)-ball, \(S^ n\) the Euclidean unit \(n\)-sphere and \(u^*(x)=({x\over | x|},0))\). In particular, \(u^*\) is a weakly harmonic map; i.e., a weak solution of the Euler-Lagrange equation associated with the energy functional \(E(u) = {1\over 2}\int| Du|^ 2\). The main aim of this paper is to replace \(E(u)\) by the negative- exponential energy functional \(NE(u)=\int e^{{1\over 2}| Du|^ 2}\); the equator map \(u^*\) is then shown to be an unstable critical point of \(NE(u)\) for all \(n \geq 2\).
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 91449
zbMATH Keywords: equator map
zbMATH Keywords: regularity
zbMATH Keywords: harmonic maps
zbMATH Keywords: unit \(n\)-ball
zbMATH Keywords: unit \(n\)-sphere
zbMATH Keywords: Euler-Lagrange equation
zbMATH Keywords: unstable critical point
Wikidata QID: Q114213972
reviewed by: Andrea Ratto
MaRDI profile type: Publication
cites work: Singularities of energy-minimizing maps from the ball to the sphere
cites work: Another Report on Harmonic Maps
cites work: Harmonic Mappings of Riemannian Manifolds
cites work: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
cites work: Q3331814
cites work: Q3733833
cites work: Existence and partial regularity of static liquid crystal configurations
cites work: A remark on \(H^ 1\) mappings
cites work: Mappings minimizing theLp norm of the gradient
cites work: Q3782310
cites work: An existence theorem for harmonic mappings of Riemannian manifolds
cites work: Q3663717
cites work: Q3247767
cites work: Q3797914
cites work: A regularity theory for harmonic maps
cites work: Regularity of minimizing harmonic maps into the sphere
cites work: Boundary regularity and the Dirichlet problem for harmonic maps
OpenAlex ID: W2009878654
Recommended article: Q4391987
Recommended article: Q5465477
Recommended article: Q3191327
Recommended article: Q4359506
Recommended article: On some functional-differential inequalities related to the exponential mapping
Recommended article: Quasiconformal mappings and exponentially integrable functions
Recommended article: Q3105079
Recommended article: On the Stability of the Equator Map for Higher Order Energy Functionals
Recommended article: The double exponential map on spaces of constant curvature
Recommended article: The Derivative of the Exponential Map
description: scientific article; zbMATH DE number 91449