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

created by martinazz on 21 Nov 2010
modified on 17 Jul 2018

[BibTeX]

Accepted Paper

Inserted: 21 nov 2010
Last Updated: 17 jul 2018

Journal: Journal Funct. Anal.
Year: 2011

ArXiv: 1011.5440 PDF

Abstract:

For any n>1 we give an explicit example of an n-axially symmetric Cartesian current in B3 x S2 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.