Related papers: Energy capacity inequalities via an action selecto…

In this paper, we first introduce the concept of symmetrical symplectic capacity for symmetrical symplectic manifolds, and by using this symmetrical symplectic capacity theory we prove that there exists at least one symmetric closed…

Let $\text{Ham(M)}$ be the group of Hamiltonian symplectomorphisms of a quantizable, compact, symplectic manifold $(M,\omega)$. We prove the existence of an action integral around loops in $\text{Ham(M)}$, and determine the value of this…

The (local) invariant symplectic action functional $\A$ is associated to a Hamiltonian action of a compact connected Lie group $\G$ on a symplectic manifold $(M,\omega)$, endowed with a $\G$-invariant Riemannian metric $<\cdot,\cdot>_M$. It…

We introduce the Hofer-Zehnder $G$-semicapacity $c_{HZ}^G(M,\om)$ of a symplectic manifold $(M,\om)$ with respect to a subgroup $G \subset \pi_1(M)$ ($c_{HZ}(M,\om) \leq c^G_{HZ}(M,\om)$) and prove that if $(M,\om)$ is tame and there exists…

We use the minimal coupling procedure of Sternberg and Weinstein and our pseudo-symplectic capacity theory to prove that every closed symplectic submanifold in any symplectic manifold has an open neighborhood with finite ($\pi_1$-sensitive)…

We prove a coisotropic intersection result and deduce the following: 1. Lower bounds on the displacement energy of a subset of a symplectic manifold, in particular a sharp stable energy-Gromov-width inequality. 2. A stable non-squeezing…

We classify symplectic non-Hamiltonian circle actions on compact connected symplectic 4-manifolds, up to equivariant symplectomorphisms. Namely, we define a set of invariants, show that the set is complete, and determine which values are…

In this article, we provide an exposition about symplectic toric manifolds, which are symplectic manifolds $(M^{2n}, \omega)$ equipped with an effective Hamiltonian $\mathbb{T}^n\cong (S^1)^n$-action. We summarize the construction of $M$ as…

In this paper we study the size of the fixed point set of a Hamiltonian diffeomorphism on a closed symplectic manifold which is both rational and weakly monotone. We show that there exists a non-trivial cycle of fixed points whenever the…

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…

In this paper we introduce invariants of semi-free Hamiltonian actions of $S\sp 1$ on compact symplectic manifolds (which satisfy some technical conditions related to positivity) using the space of solutions to certain gauge theoretical…

Let $M$ be a compact manifold with an effective semi-free circle action whose fixed point set has trivial normal bundle. We prove that its cotangent bundle endowed with the canonical symplectic form has bounded Hofer-Zehnder sensitive…

We investigate the existence of homotopy comoment maps (comoments) for high-dimensional spheres seen as multisymplectic manifolds. Especially, we solve the existence problem for compact effective group actions on spheres and provide…

We study meromorphic actions of unipotent complex Lie groups on compact K\"ahler manifolds using moment map techniques. We introduce natural stability conditions and show that sets of semistable points are Zariski-open and admit geometric…

We give a systematic presentation of the stability theory in the non-algebraic Kaehlerian geometry. We introduce the concept of "energy complete Hamiltonian action". To an energy complete Hamiltonian action of a reductive group G on a…

Let $M$ be a $2n$-dimensional closed symplectic manifold admitting a Hamiltonian circle action with isolated fixed points. We show that if $M$ contains an $S^1$-invariant symplectic hypersurface $D$ such that $M\setminus D$ is a homology…

Assume $(M, \omega)$ is a connected, compact 6 dimensional symplectic manifold equipped with a semi-free Hamiltonian circle action, such that the fixed point set consists of isolated points or compact orientable surfaces. We restrict…

We consider a connected symplectic manifold $M$ acted on properly and in a Hamiltonian fashion by a connected Lie group $G$. Inspired to the recent paper \cite{gb2}, see also \cite{ch} and \cite{pacini}, we study Lagrangian orbits of…

We consider compact connected six dimensional symplectic manifolds with Hamiltonian SU(2) or SO(3) actions with cyclic principal stabilizers. We classify such manifolds up to equivariant symplectomorphisms.

In this paper, we classify Hamiltonian $S^1$-actions on compact, four dimensional symplectic orbifolds that have isolated singular points with cyclic orbifold structure groups, thus extending the classification due to Karshon to the…