## Abstract In this paper, we introduce a new energy functional, $\bar \partial $βenergy functional, instead of the total energy functional to investigate the uniqueness of harmonic maps with respect to any given metric on the unit disk. Even in the setting that the Hopf differentials of harmonic m
Harmonic maps and uniqueness of axisymmetric monopole solutions
β Scribed by P.O. Mazur; E. Richter
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 343 KB
- Volume
- 109
- Category
- Article
- ISSN
- 0375-9601
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π SIMILAR VOLUMES
We present an elementary argument of the regularity of weak harmonic maps of a surface into the spheres, as well as the partial regularity of stationary harmonic maps of a higher-dimensional domain into the spheres. The argument does not make use of the structure of Hardy spaces.
A growth lemma for certain discrete symmetric Laplacians defined on a lattice Z d Ξ΄ = Ξ΄Z d β R d with spacing Ξ΄ is proved. The lemma implies a De Giorgi theorem, that the harmonic functions for these Laplacians are equi-HΓΆlder continuous, Ξ΄ β 0. These results are then applied to establish regularity