A priori estimates for D4 and F4 Toda systems

Abstract In this article we establish the a priori bounds of the Toda systems with arbitrarily many singular sources associated to the simple Lie algebras of type D 4 and F 4 , extending the previous works of Lin et al. [27] , [20] , [24] for the A n , B n , C n and G 2 type Lie algebras. The problem of obtaining a priori estimates can be reduced to locating the local mass of blowup solutions. The key step is to calculate the local mass near each blowup points efficiently. A precise estimate on the total mass of entire solutions of Toda systems with many singular sources is an indispensable step in our argument.