A variational characterization of $J$-holomorphic curves in symplectic manifolds

Abstract

In this paper, we prove that if the area functional of a surface ${\Sigma }^2$ in a symplectic manifold $(M^{2n},\bar{\omega })$ 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.

arXiv commentRevised version, 29 Pages

References in corpus (1)

• Transcendental Kähler Cohomology Classes