2012/11/29 by Claudio Arezzo, Jun Sun, Arezzo, Claudio +1
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.1211.7016
In this paper, we prove that if the area functional of a surface Σ2 in a symplectic manifold (M2n,ω) has a critical point or has a compatible stable point in the same cohomology class, then it must be J-holomorphic. Inspired by a classical result of Lawson-Simons, we show how various restrictions of the stability assumption to variations of metrics in the space "projectively induced" metrics are enough to give the desired conclusion.