On The 1+2 Dimensional Landau-Lifshitz Equation
  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. 
Qing Ding