A note on $n$-axially symmetric harmonic maps from $B^3$ to $S^2$ minimizing the relaxed energy

Details A note on $n$-axially symmetric harmonic maps from $B^3$ to $S^2$ minimizing the relaxed energy A note on $n$-axially symmetric harmonic maps from $B^3$ to $S^2$ minimizing the relaxed energy

2010-11-24

arxiv.org/abs/1011.5440v2

Mathematics

Analysis of PDEs

17 pages

Scientific paper

10.1016/j.jfa.2011.07.022

For any n>1 we give an explicit example of an n-axially symmetric Cartesian
current in B^3 x S^2 with non-trivial vertical part and non-constant graph part
minimizing the relaxed Dirichlet energy among the n-axially symmetric Cartesian
currents with the same boundary. This stands in sharp contrast with a results
of Hardt, Lin and Poon for the case n=1.

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