We shall continue discussing J. P. Demailly's proposal of several systems of nonlinear elliptic PDE to prove Griffiths conjecture. We have studied two of these systems on the Vortex bundle. The Vortex bundle is a rank two vector bundle on a complex surface with high symmetry. In this talk, we shall discuss the existence result of these systems of PDE on the Vortex bundle.
Demailly's system, Vortex bundle, Nonlinear elliptic PDE
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