für Mathematik in den Naturwissenschaften Leipzig Regularity and blow - up analysis for

If u ∈ H(M,N) is a weakly J-holomorphic map from a compact without boundary almost hermitian manifold (M, j, g) into another compact without boundary almost hermitian manifold (N, J, h). Then it is smooth near any point x where Du has vanishing Morrey norm M2,2m−2, with 2m =dim(M). Hence H2m−2measure of the singular set for a stationary J-holomorphic map is zero. Blow-up analysis and the energy quantization theorem are established for stationary J-holomorphic. Connections between stationary Jholomorphic maps and stationary harmonic maps are given for either almost Kähler manifolds M and N or symmetric ∇hJ . §