Minimizing area among Lagrangian surfaces: the mapping problem

Details Minimizing area among Lagrangian surfaces: the mapping problem Minimizing area among Lagrangian surfaces: the mapping problem

2000-08-28

arxiv.org/abs/math/0008244v2

Mathematics

Differential Geometry

Abstract added in migration (from introduction)

Scientific paper

This paper introduces a geometrically constrained variational problem for the area functional. We consider the area restricted to the langrangian surfaces of a Kaehler surface, or, more generally, a symplectic 4-manifold with suitable metric, and study its critical points and in particular its minimizers. We apply this study to the problem of finding canonical representatives of the lagrangian homology (that part of the homology generated by lagrangian cycles).

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