Local solution to the $G_{2}-$monopole equation with prescribed tangent   cone and $G_{2}-$structure
  For any locally defined $G_{2}-$structure and Hermitian-Yang-Mills connection on $S^{6}$, the $G_{2}-$monopole equation always admits a local solution that is asymptotic to the HYM-connection. 
Yuanqi Wang
math.DG math-ph math.AP math.MP