We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
56/2002
Regularity and blow-up analysis for $J$-holomorphic maps
Changyou Wang
Abstract
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 $\nabla^h J$.