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A variational characterization of J-holomorphic curves

  • Claudio Arezzo EMAIL logo and Jun Sun
Published/Copyright: November 22, 2013

Abstract

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.

Funding source: FIRB

Award Identifier / Grant number: “Geometria Differenziale Complessa e Dinamica Olomorfa”

Received: 2013-2-19
Revised: 2013-7-26
Published Online: 2013-11-22
Published in Print: 2015-12-1

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