Zobrazeno 1 - 10
of 39
pro vyhledávání: '"Hryniewicz, Umberto L."'
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 combination of pseudo-holomorphic curve methods with some elementary
Externí odkaz:
http://arxiv.org/abs/2012.12055
We introduce numerical invariants of contact forms in dimension three and use asymptotic cycles to estimate them. As a consequence, we prove a version for Anosov Reeb flows of results due to Hutchings and Weiler on mean actions of periodic points. Th
Externí odkaz:
http://arxiv.org/abs/2006.06266
We exhibit sufficient conditions for a finite collection of periodic orbits of a Reeb flow on a closed $3$-manifold to bound a positive global surface of section with genus zero. These conditions turn out to be $C^\infty$-generically necessary. Moreo
Externí odkaz:
http://arxiv.org/abs/1912.01078
Autor:
Hryniewicz, Umberto L.
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 to Fried, recast in terms of invariant measures instead of homology d
Externí odkaz:
http://arxiv.org/abs/1904.12416
Publikováno v:
Trans. Amer. Math. Soc. 374 (2021), 1815-1845
We prove that the systolic ratio of a sphere of revolution $S$ does not exceed $\pi$ and equals $\pi$ if and only if $S$ is Zoll. More generally, we consider the rotationally symmetric Finsler metrics on a sphere of revolution which are defined by sh
Externí odkaz:
http://arxiv.org/abs/1808.06995
We survey some recent developments in the quest for global surfaces of section for Reeb flows in dimension three using methods from Symplectic Topology. We focus on applications to geometry, including existence of closed geodesics and sharp systolic
Externí odkaz:
http://arxiv.org/abs/1712.01925
Publikováno v:
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 19 (2019), 1561-1582
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 co-orientable contact structure on any closed three-manifold is defin
Externí odkaz:
http://arxiv.org/abs/1709.01621
We prove the transversality result necessary for defining local Morse chain complexes with finite cyclic group symmetry. Our arguments use special regularized distance functions constructed using classical covering lemmas, and an inductive perturbati
Externí odkaz:
http://arxiv.org/abs/1702.04609
The first result of this paper is that every contact form on $\mathbb{R} P^3$ sufficiently $C^\infty$-close to a dynamically convex contact form admits an elliptic-parabolic closed Reeb orbit which is $2$-unknotted, has self-linking number $-1/2$ and
Externí odkaz:
http://arxiv.org/abs/1505.02713
Publikováno v:
Math. Ann. 367 (2017), 701-753
For a Riemannian metric $g$ on the two-sphere, let $\ell_{\min}(g)$ be the length of the shortest closed geodesic and $\ell_{\max}(g)$ be the length of the longest simple closed geodesic. We prove that if the curvature of $g$ is positive and sufficie
Externí odkaz:
http://arxiv.org/abs/1410.7790