30 citations · 244 across the 39 of their papers we have counts for
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A symplectic dynamics proof of the degree-genus formula
Peter Albers, Hansjörg Geiges, Kai Zehmisch
We classify global surfaces of section for the Reeb flow of the standard contact form on the 3-sphere, defining the Hopf fibration. As an application, we prove the degree-genus for…
Pseudorotations of the 2-disc and Reeb flows on the 3-sphere
Peter Albers, Hansjörg Geiges, Kai Zehmisch
We use Lerman's contact cut construction to find a sufficient condition for Hamiltonian diffeomorphisms of compact surfaces to embed into a closed 3-manifold as Poincaré return map…
Odd-symplectic forms via surgery and minimality in symplectic dynamics
Hansjörg Geiges, Kai Zehmisch
We construct an infinite family of odd-symplectic forms (also known as Hamiltonian structures) on the 3-sphere that do not admit a symplectic cobordism to the standard contact stru…
Reeb dynamics inspired by Katok's example in Finsler geometry
Peter Albers, Hansjörg Geiges, Kai Zehmisch
Inspired by Katok's examples of Finsler metrics with a small number of closed geodesics, we present two results on Reeb flows with finitely many periodic orbits. The first result i…
Finsler geodesics, periodic Reeb orbits, and open books
Max Dörner, Hansjörg Geiges, Kai Zehmisch
We survey some results on the existence (and non-existence) of periodic Reeb orbits on contact manifolds, both in the open and closed case. We place these statements in the context…
From a Reeb orbit trap to a Hamiltonian plug
Hansjörg Geiges, Nena Röttgen, Kai Zehmisch
We present a simple construction of a plug for Hamiltonian flows on hypersurfaces of dimension at least five by doubling a trap for Reeb orbits.