4 papers
Global surfaces of section with positive genus for dynamically convex Reeb flows
Umberto L. Hryniewicz, Pedro A. S. Salomão, Richard Siefring
We establish some new existence results for global surfaces of section of dynamically convex Reeb flows on the three-sphere. These sections often have genus, and are the result of…
A note on Schwartzman-Fried-Sullivan Theory, with an application
Umberto L. Hryniewicz
We prove a theorem on the existence of global surfaces of section with prescribed spanning orbits and homology class. This result is a modification and a refinement of a result due…
Sharp systolic inequalities for Riemannian and Finsler spheres of revolution
Alberto Abbondandolo, Barney Bramham, Umberto L. Hryniewicz +1
We prove that the systolic ratio of a sphere of revolution does not exceed and equals if and only if is Zoll. More generally, we consider the rotationally symmetric…
Closed Reeb orbits on the sphere and symplectically degenerate maxima
Viktor L. Ginzburg, Doris Hein, Umberto L. Hryniewicz +1
We show that the existence of one simple closed Reeb orbit of a particular type (a symplectically degenerate maximum) forces the Reeb flow to have infinitely many periodic orbits.…