Length and volume in contact three-manifolds

Length and volume in contact three-manifolds

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Michael Hutchings, University of California - Berkeley
Fine Hall 314

We give an introduction to a theorem (joint with Dan Cristofaro-Gardiner and Vinicius Ramos) that relates the volume of a contact three-manifold to the lengths of certain collections of closed orbits of the Reeb vector field. This implies that the Reeb vector field always has at least two closed orbits. We also discuss a conjecture on the existence of a Reeb orbit which is short with respect to the volume.