39 citations · 73 across the 10 of their papers we have counts for
12 papers
Rigidity of coarsely minimal Reeb flows
Barney Bramham, Jacobus S. de Pooter
We introduce the notion of a coarsely minimal Reeb flow, generalizing the notion of minimal geodesic flow, and prove the following rigidity theorem: That a coarsely minimal Reeb fl…
Spectral invariants for non-compactly supported Hamiltonians on the disc, and an application to the mean action spectrum
Barney Bramham, Abror Pirnapasov
For a symplectic isotopy on the two-dimensional disc we show that the classical spectral invariants of Viterbo [20] can be extended in a meaningful way to {\it non-compactly} suppo…
On pseudo-rotations of the annulus with generic rotation number
Barney Bramham, Zhiyuan Zhang
We show that for a Baire generic rotation number , the set of area preserving -pseudo-rotations of the annulus with rotation nu…
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…
Systolic ratio, index of closed orbits and convexity for tight contact forms on the three-sphere
Alberto Abbondandolo, Barney Bramham, Umberto Hryniewicz +1
We construct a dynamically convex contact form on the three-sphere whose systolic ratio is arbitrarily close to 2. This example is related to a conjecture of Viterbo, whose validit…
Contact forms with large systolic ratio in dimension three
Alberto Abbondandolo, Barney Bramham, Umberto L. Hryniewicz +1
The systolic ratio of a contact form on a closed three-manifold is the quotient of the square of the shortest period of closed Reeb orbits by the contact volume. We show that every…