Electron. J. Diff. Eqns., Vol. 2000(2000), No. 45, pp. 1-13.

Some constancy results for harmonic maps from non-contractable domains into spheres

Kewei Zhang

We use the Pohozaev identity on sub-domains of a Euclidean r-neighbourhood for a closed or broken curve to show that harmonic maps from such domains into spheres with constant boundary value remain constant.

Submitted March 31, 2000. Published June 14, 2000.
Math Subject Classifications: 58E20 35J65 35J60.
Key Words: harmonic maps, uniqueness, Pohozaev identity, closed geodesics, tubular neighbourhoods.

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Kewei Zhang
Department of Mathematics
Macquarie University
Sydney, Australia
e-mail address: kewei@ics.mq.edu.au

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