J-holomorphic Curves And Periodic Reeb Orbits

Details J-holomorphic Curves And Periodic Reeb Orbits J-holomorphic Curves And Periodic Reeb Orbits

2000-04-07

arxiv.org/abs/math/0004037v4

Mathematics

Differential Geometry

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Scientific paper

We study the $J-$holomorphic curves in the symplectization of the contact
manifolds and prove that there exists at least one periodic Reeb orbits in any
closed contact manifold with any contact form by using the well-known Gromov's
nonlinear Fredholm alternative for $J-$holomorphic curves. As a corollary, we
give a complete solution on the well-known Weinstein conjecture.

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