Contact topology and hydrodynamics II: solid tori

Details Contact topology and hydrodynamics II: solid tori Contact topology and hydrodynamics II: solid tori

1999-07-17

arxiv.org/abs/math/9907112v1

Mathematics

Symplectic Geometry

14 pages, 1 figure

Scientific paper

We prove the existence of periodic orbits for steady $C^\omega$ Euler flows on all Riemannian solid tori. By using the correspondence theorem from part I of this series, we reduce the problem to the Weinstein Conjecture for solid tori. We prove the Weinstein Conjecture on the solid torus via a combination of results due to Hofer et al. and a careful analysis of tight contact structures on solid tori.

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