Related papers: Regular Symplectic Foliations on Closed manifolds

We generalize symplectic convexity theorems for Hamiltonian actions with proper momentum maps to symplectic actions on orbifolds with mod-$\Gamma$ proper momentum maps.

A famous result of Jurgen Moser states that a symplectic form on a compact manifold cannot be deformed within its cohomology class to an inequivalent symplectic form. It is well known that this does not hold in general for noncompact…

The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces. More precisely, we will show that (1) if $(M,\omega)$ admits a…

In this note, we propose a symplectic algorithm for the stable manifolds of the Hamilton-Jacobi equations combined with an iterative procedure in [Sakamoto-van~der Schaft, IEEE Transactions on Automatic Control, 2008]. Our algorithm…

Given a closed symplectic manifold, we study when the Lefschetz decomposition induced by the $\mathfrak{sl}(2;\mathbb{R})$-representation yields a decomposition of the de Rham cohomology. In particular, this holds always true for the second…

We study codimension one smooth foliations with Morse type singularities on closed ma-nifolds. We obtain a description of the manifold in case the number of centers in greater then the number of saddles. This result relies on and extends…

In this paper, we study the global geometry of complete, constant mean curvature hypersurfaces embedded in n-manifolds. More precisely, we give conditions that imply properness of such surfaces and prove the existence of fixed size…

We study the rigidity and flexibility of symplectic embeddings of simple shapes. It is first proved that under the condition $r_n^2 \le 2 r_1^2$ the symplectic ellipsoid $E(r_1, ..., r_n)$ with radii $r_1 \le ... \le r_n$ does not embed in…

In this paper, we complete the classification of six-dimensional closed monotone symplectic manifolds admitting semifree Hamiltonian $S^1$-actions. We also show that every such manifold is $S^1$-equivariantly symplectomorphic to some…

In this paper, we treat an open problem related to the number of periodic orbits of Hamiltonian diffeomorphisms on closed symplectic manifolds, so-called generic Conley conjecture. Generic Conley conjecture states that generically…

In this paper we will show how to construct holomorphic L^{p}-functions on unbranched coverings of strongly pseudoconvex manifolds. Also, we prove some extension and approximation theorems for such functions.

We prove the following theorem for Holomorphic Foliations in compact complex kaehler manifolds: if there is a compact leaf with finite holonomy, then every leaf is compact with finite holonomy. As corollary we reobtain stability theorems…

We prove that smooth cube manifolds have normal smooth structures.

Let $\varphi_t : M \to M$ be a flow on a smooth closed connected manifold $M$ that preserves and expands a foliation $F$. We establish a theorem of propagation of regularity along the leaves of $F$ for sections of vector bundles satisfying…

Let $(M,\omega)$ be a closed $2n$-dimensional semifree Hamiltonian $S^1$-manifold with only isolated fixed points. We prove that a density function of the Duistermaat-Heckman measure is log-concave. Moreover, we prove that $(M,\omega)$ and…

Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary…

Let $X$ be a compact connected Riemann surface, $D\, \subset\, X$ a reduced effective divisor, $G$ a connected complex reductive affine algebraic group and $H_x\, \subsetneq\, G_x$ a Zariski closed subgroup for every $x\, \in\, D$. A framed…

A fundamental result of Banyaga states that the Hamiltonian diffeomorphism group of a closed symplectic manifold is perfect. We refine this result by proving that, locally in the $C^\infty$ topology, the number of commutators needed to…

This is the second in a series of papers on standard monomial theory and invariant theory of arc spaces. For any algebraically closed field $K$, we construct a standard monomial basis for the arc space of the Pfaffian variety over $K$. As…

A symplectic semitoric manifold is a symplectic $4$-manifold endowed with a Hamiltonian $(S^1 \times \mathbb{R})$-action satisfying certain conditions. The goal of this paper is to construct a new symplectic invariant of symplectic…