Regularity and blow-up analysis for J-holomorphic maps
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Submission date: 15. Jul. 2002
published in: Communications in contemporary mathematics, 5 (2003) 4, p. 671-704
DOI number (of the published article): 10.1142/S0219199703001063
Keywords and phrases: j-holomorphic spheres, j-holomorphic maps, energy quantization, rectifiablity, stationarity
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If 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 , with 2m=dim(M). Hence measure 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 maps. Connections between stationary J- holomorphic maps and stationary harmonic maps are given for either almost Kähler manifolds M and N or symmetric .