File(s) under permanent embargo
Spherical twists, stationary loops and harmonic maps from generalised annuli into spheres
Let X ? Rn be a generalised annulus and consider the Dirichlet energy functional E[u; X] := 1/2?X |?u(x)|²dx, on the space of admissible maps A?(X) = u ? W²,¹ (X, Sn¯¹) : u|?X = ? . Here ? ? C(?X, Sn¯¹) is fixed and A?(X) is non-empty. In this paper we introduce a class of maps referred to as spherical twists and examine them in connection with the Euler–Lagrange equation associated with E[·, X] on A?(X) [the so-called harmonic map equation on X]. The main result here is an interesting discrepancy between even and odd dimensions. Indeed for even n subject to a compatibility condition on ? the latter system admits infinitely many smooth solutions modulo isometries whereas for odd n this number reduces to one or none. We discuss qualitative features of the solutions in view of their novel and explicit representation through the exponential map of the compact Lie group SO(n).
History
Publication status
- Published
File Version
- Published version
Journal
Nonlinear Differential Equations and ApplicationsISSN
1021-9722Publisher
Springer VerlagExternal DOI
Issue
1Volume
19Page range
79-95Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2017-11-07First Compliant Deposit (FCD) Date
2017-11-06Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC