Related papers: Symplectic stability on manifolds with cylindrical…

We study a stabilization of the symplectic category introduced by A. Weinstein as a domain for the geometric quantization functor. The symplectic category is a topological category with objects given by symplectic manifolds, and morphisms…

In symplectic geometry, symplectic invariants are useful tools in studying symplectic phenomena. Hofer-Zehnder capacity and displacement energy are important symplectic invariants. Usher proved the so-called sharp energy-capacity inequality…

For any symplectic manifold, Hamiltonian diffeomorphism group contains a subset which consists of times one flows of autonomous(time-independent) Hamiltonian vector fields. Polterovich and Shelukhin proved that the complement of autonomous…

We discuss stability of spherically symmetric static solutions in Newtonian limit of Jordan, Brans-Dicke field equations. The behavior of the stable equilibrium solutions for the spherically symmetric configurations considered here, it…

Consider the tangent bundle of a Riemannian manifold $(M,g)$ of dimension $n\geq3$ admitting a metric of negative curvature (not necessarily equal to $g$) endowed with a twisted symplectic structure defined by a closed 2-form on $M$. We…

We consider the dynamics of semiflows of patterns on unbounded domains that are equivariant under a noncompact group action. We exploit the unbounded nature of the domain in a setting where there is a strong `global' norm and a weak `local'…

In this article we extend several foundational results of the theory of complete minimal surfaces of finite index in the Euclidean space to minimal surfaces in asymptotically flat manifolds and, more generally, to marginally outer-trapped…

We study the Morse-Novikov cohomology and its almost-symplectic counterpart on manifolds admitting locally conformally symplectic structures. More precisely, we introduce lcs cohomologies and we study elliptic Hodge theory, dualities, Hard…

Given an affine Poisson algebra, that is singular one may ask whether there is an associated symplectic form. In the smooth case the answer is obvious: for the symplectic form to exist the Poisson tensor has to be invertible. In the…

We prove a smooth compactness theorem for the space of elasticae, unless the limit curve is a straight segment. As an application, we obtain smooth stability results for minimizers with respect to clamped boundary data.

We introduce the notion of a symplectic capacity relative to a coisotropic submanifold of a symplectic manifold, and we construct two examples of such capacities through modifications of the Hofer-Zehnder capacity. As a consequence, we…

We give an example of a symplectic manifold with a stable hypersurface such that nearby hypersurfaces are typically unstable.

Because of Minty's classical correspondence between firmly nonexpansive mappings and maximally monotone operators, the notion of a firmly nonexpansive mapping has proven to be of basic importance in fixed point theory, monotone operator…

I construct the real counterparts (which I call Borel-Bott classes) of the R/Z classes constructed in "Characteristic classes in symplectic topology", to appear, in the cohomology of volume-preserving and symplectomorhisms of a compact…

We prove that the generalized symplectic capacities recognize objects in symplectic categories whose objects are of the form $(M, \omega)$, such that $M$ is a compact and 1-connected manifold, $\omega$ is an exact symplectic form on $M$,…

Many of the existing results for closed Hamiltonian G-manifolds are based on the analysis of the corresponding Hamiltonian functions using Morse-Bott techniques. In general such methods fail for non-compact manifolds or for manifolds with…

We provide topological obstructions to the existence of orbit cylinders of symmetric orbits, for mechanical systems preserved by antisymplectic involutions (e.g. the restricted three-body problem). Such cylinders induce continuous paths…

An embedding $\varphi \colon (M_1, \omega_1) \to (M_2, \omega_2)$ (of symplectic manifolds of the same dimension) is called $\epsilon$-symplectic if the difference $\varphi^* \omega_2 - \omega_1$ is $\epsilon$-small with respect to a fixed…

A complete embedding is a symplectic embedding $\iota:Y\to M$ of a geometrically bounded symplectic manifold $Y$ into another geometrically bounded symplectic manifold $M$ of the same dimension. When $Y$ satisfies an additional finiteness…

We introduce a new map between configuration spaces of points in a background manifold - the replication map - and prove that it is a homology isomorphism in a range with certain coefficients. This is particularly of interest when the…