关键词: Heisenberg group, energy minimizer, Legendrian map, regularity, singularity

Abstract:

In this paper, the properties of the maps for the
Heisenberg group targets are studied. For $u \in W^{1,\alpha
}(\Omega, {\bf H}^m)$,  some Poincar\'e type inequalities are proved.
For the energy minimizers,  the $\epsilon$-regularity theorems
and the singularity theorems are obtained.

Key words: Heisenberg group, energy minimizer, Legendrian map, regularity, singularity