  By using the geometric concept of PDEs with prescribed curvature
representations, we show that the 1+2 dimensional Landau-Lifshitz equation is
gauge equivalent to a 1+2 dimensional nonlinear Schr\"odinger-type system.
  From the nonlinear Schr\"odinger-type system, we construct blowing up
$H^3({\bf R}^2)$-solutions to the 1+2 dimensional Landau-Lifshitz equation,
which reveals the blow up phenomenon of the equation.
