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arXiv · 1011.5440

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

Luca Martinazzi
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Abstract

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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Luca Martinazzi. 2010-11-24. A note on $n$-axially symmetric harmonic maps from $B^3$ to $S^2$ minimizing the relaxed energy. https://doi.org/10.1016/j.jfa.2011.07.022

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