A remark on a theorem of Schoen and Wolfson

Details A remark on a theorem of Schoen and Wolfson A remark on a theorem of Schoen and Wolfson

2003-01-21

arxiv.org/abs/math/0301223v2

Mathematics

Differential Geometry

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Scientific paper

Let $ l : \Sigma \to X$ be a weakly Lagrangian map of a compact orientable surface $ \Sigma$ in a K\"ahler surface $ X$ which is area minimizing in its homotopy class of maps in $ W^{1,2}(\Sigma, X)$, the Sobolev space of maps of square integrable first derivative. Schoen and Wolfson showed such $ l$ is Lipschitz, and it is smooth except at most at finitely many points of Maslov index 1 or -1. In this note, we observe if in addition c_1(X)[l]=0, $ l$ is smooth everywhere. Here $ c_1(X)$ is the first Chern class of $ X$.

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