University of Sussex
Browse

File(s) under permanent embargo

Spherical twists, stationary loops and harmonic maps from generalised annuli into spheres

journal contribution
posted on 2023-06-09, 08:40 authored by Ali TaheriAli Taheri
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 Applications

ISSN

1021-9722

Publisher

Springer Verlag

Issue

1

Volume

19

Page range

79-95

Department 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

2017-11-07

First Compliant Deposit (FCD) Date

2017-11-06

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports