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Contact topology and hydrodynamics II: solid tori

Published online by Cambridge University Press:  19 June 2002

JOHN ETNYRE  and
ROBERT GHRIST
JOHN ETNYRE
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104-6395, USA (e-mail: etnyre@math.upenn.edu)
ROBERT GHRIST
Affiliation:
School of Mathematics & CDSNS, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA (e-mail: ghrist@math.gatech.edu)
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Abstract

We prove the existence of periodic orbits for steady real-analytic 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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 3 , June 2002 , pp. 819 - 833
Copyright
2002 Cambridge University Press

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