A remark on a theorem of Schoen and Wolfson

2003/01/21 by Sung Ho Wang, Wang, Sung Ho
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.math/0301223

This paper is incorrect. It is withdrawn by the author

openalex publication_date 2003/01/21 · arxiv created 2012/01/20 · arxiv updated 2012/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let l : Σ→ X be a weakly Lagrangian map of a compact orientable surface Σ in a Kähler surface X which is area minimizing in its homotopy class of maps in W^1,2(Σ, 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 c₁(X)[l]=0, l is smooth everywhere. Here c₁(X) is the first Chern class of X.

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