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MiS Preprint

Regularity and blow-up analysis for $J$-holomorphic maps

Changyou Wang


If $u\in H^1(M,N)$ 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 ${\mathcal M}^{2,2m-2}$, with $2m=$dim$(M)$. Hence $H^{2m-2}$ 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 $\nabla^h J$.

j-holomorphic spheres, j-holomorphic maps, energy quantization, rectifiablity, stationarity

Related publications

2003 Repository Open Access
Chaofeng Wang

Regularity and blow-up analysis for J-holomorphic maps

In: Communications in contemporary mathematics, 5 (2003) 4, pp. 671-704