In this paper, we prove that if the area functional of a surface in a symplectic manifold 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.
A variational characterization of J-holomorphic curves / Arezzo, Claudio; J., Sun. - In: JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK. - ISSN 1435-5345. - 709:(2015), pp. 171-200. [10.1515/crelle-2013-0097]
A variational characterization of J-holomorphic curves
AREZZO, Claudio;
2015-01-01
Abstract
In this paper, we prove that if the area functional of a surface in a symplectic manifold 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.File in questo prodotto:
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