Contact topology and hydrodynamics II: solid tori
Abstract
Description
We prove the existence of periodic orbits for steady $C^ω$ 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.
14 pages, 1 figure
14 pages, 1 figure