Related papers: A note on Schwartzman-Fried-Sullivan Theory, with …
Schoen-Webster theorem asserts a pseudoconvex CR manifold whose automorphism group acts non properly is either the standard sphere or the Heisenberg space. The purpose of this paper is to survey successive works around this result and then…
Using the notion of Levi form of a smooth distribution, we discuss the local and the global problem of existence of one horizontal section of a smooth vector bundle endowed with a horizontal distribution. The analysis will lead to the…
The generalization of Bertrand's theorem to abstract surfaces of revolution without "equators" is proved. We prove a criterion for the existence on such a surface of exactly two central potentials (up to an additive and a multiplicative…
We develop connections between the qualitative dynamics of Hamiltonian isotopies on a surface $\Sigma$ and their chain-level Floer theory using ideas drawn from Hofer-Wysocki-Zehnder's theory of finite energy foliations. We associate to…
We investigate global continuation of periodic orbits of a differential equation depending on a parameter, assuming that a closed 1-form satisfying certain properties exists. We begin by extending the global continuation theory of…
In this paper we propose a computational approach to proving the Birkhoff conjecture on the restricted three-body problem, which asserts the existence of a disk-like global surface of section. Birkhoff had conjectured this surface of…
For every nontrivial free homotopy class $\alpha$ of loops in every closed connected Riemannian manifold $M$, we prove existence of a noncontractible 1-periodic orbit, for every compactly supported time-dependent Hamiltonian on the open…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
This is the first paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. The theory will be illustrated in upcoming papers by applications to Floer Theory, Gromov-Witten Theory and…
In this note, we study the Gehring link problem in the round sphere, which motives our study of the width of a band in positively curved manifolds. Using the same idea, we are able to get a sphere theorem for hypersurface in in the round…
A projectability result is proved for surfaces of prescribed mean curvature (shortly called $H$-surfaces) spanned in a partially free boundary configuration. Hereby, the $H$-surface is allowed to meet the support surface along its free…
We consider surfaces with a double elliptic fibration, with two sections. We study the orbits under the induced translation automorphisms proving that, under natural conditions, the finite orbits are confined to a curve. This goes in a…
Here we present a rigidity result in a global (semi-global, homotopy) setting for a restrictive class of polytopes, those that can be inscribed in a unit sphere, with some additional conditions. The proof of the rigidity result for cabled…
We introduce in this paper a field theory on symplectic manifolds that are fibered over a real surface with interior marked points and cylindrical ends. We assign to each such object a morphism between certain tensor products of quantum and…
We classify global surfaces of section for flows on 3-manifolds defining Seifert fibrations. We discuss branched coverings -- one way or the other -- between surfaces of section for the Hopf flow and those for any other Seifert fibration of…
In this paper we develop an abstract theory for the Codazzi equation on surfaces, and use it as an analytic tool to derive new global results for surfaces in the space forms ${\bb R}^3$, ${\bb S}^3$ and ${\bb H}^3$. We give essentially…
We extend the classical theory of sphere theorems to the transverse geometry of Riemannian foliations. In this setting, we establish transverse analogues of the Grove-Shiohama diameter sphere theorem and of the Berger-Klingenberg…
In this paper we give a new, and shorter, proof of Huber's theorem which affirms that for a connected open Riemann surface endowed with a complete conformal Riemannian metric, if the negative part of its Gaussian curvature has finite mass,…
We introduce the notion of log-Riemann surfaces. These are Riemann surfaces given by cutting and pasting planes together isometrically, and come equipped with a holomorphic local diffeomorphism to C called the projection map, and a…
We introduce group actions on polyfolds and polyfold bundles. We prove quotient theorems for polyfolds, when the group action has finite isotropy. We prove that the sc-Fredholm property is preserved under quotient if the base polyfold is…