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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 $\nabla^h J$.

Received:
Jul 15, 2002
Published:
Jul 15, 2002
Keywords:
j-holomorphic spheres, j-holomorphic maps, energy quantization, rectifiablity, stationarity

Related publications

inJournal
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