Related papers: The Hofer question on intermediate symplectic capa…

We prove that, for every integer $n \ge 2$, a finite or infinite countable group $G$ can be embedded into a 2-generated group $H$ in such a way that the solvability of quadratic equations of length at most $n$ is preserved, i.e., every…

We prove that when $d>2$, a $d$-dimensional symplectic quotient at the zero level of a unitary circle representation $V$ such that $V^{\Sp^1}=\{0\}$ cannot be $\Z$-graded regularly symplectomorphic to the quotient of a unitary…

We show how to reduce the problem of symplectically embedding one 4-dimensional rational ellipsoid into another to a problem of embedding disjoint unions of balls into appropriate blow ups of \C P^2. For example, the problem of embedding…

We answer a question of Liokumovich-Nabutovsky-Rotman showing that if D is a Riemannian 2-disc with boundary length L, diameter d and area A << d then D can be filled by a homotopy where the lengths of the intermediate curves are bounded by…

The main theme of this paper is a relative version of the almost existence theorem for periodic orbits of autonomous Hamiltonian systems. We show that almost all low levels of a function on a geometrically bounded symplectically aspherical…

In this note we link symplectic and convex geometry by relating two seemingly different open conjectures: a symplectic isoperimetric-type inequality for convex domains, and Mahler's conjecture on the volume product of centrally symmetric…

We use positive S^1-equivariant symplectic homology to define a sequence of symplectic capacities c_k for star-shaped domains in R^{2n}. These capacities are conjecturally equal to the Ekeland-Hofer capacities, but they satisfy axioms which…

The Hofer-Zehnder theorem states that almost every hypersurface in a thickening of a hypersurface $S$ in a symplectic manifold $(M,\omega)$ carries a closed characteristic provided that $S$ bounds a compact submanifold and $(M,\omega)$ has…

The construction of the cylinder at spatial infinity for stationary spacetimes is considered. Using a specific conformal gauge and frame, it is shown that the tensorial fields associated to the conformal Einstein field equations admit…

It is proved that the potentials of the form $\beta^{2n}$ (with $n$ being integer) provide a ``bridge'' between the U(5) symmetry of the Bohr Hamiltonian with a harmonic oscillator potential (occuring for $n=1$) and the E(5) model of…

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 derive new estimates for the Gromov width of certain domains in C^2.

We present an explicit structure for the Baer invariant of a finitely generated abelian group with respect to the variety $[\mathfrak{N}_{c_1},\mathfrak{N}_{c_2}]$, for all $c_2\leq c_1\leq 2c_2$. As a consequence we determine necessary and…

We prove the existence of infinitely many periodic orbits of symplectomorphisms isotopic to the identity if they admit at least one hyperbolic periodic orbit and satisfy some condition on the flux. Our result is proved for a certain class…

The article treats some questions around Gromov's filling area conjecture. It intended to show that any filling with volume $< 2 \pi$ would not be attained and to show a local systolic inequality, implying an a priori lower estimate on the…

Quite recently, McDuff showed that the existence of a symplectic embedding of one four-dimensional ellipsoid into another can be established by comparing their corresponding sequences of ECH capacities. In this note we show that these…

A smooth counterexample to the Hamiltonian Seifert conjecture for six-dimensional symplectic manifolds is found. In particular, we construct a smooth proper function on the symplectic 2n-dimensional vector space, 2n > 4, such that one of…

We construct an open bounded star-shaped set in R^4 whose cylindrical capacity is strictly bigger than its proper displacement energy.

In any dimension $2n \ge 6$ we show that certain spaces of symplectic embeddings of a polydisk into a product $B^4 \times \Bbb R^{2(n-2)}$ of a $4$-ball and Euclidean space, are not path connected. We also show that any pair of such…

There are two themes in the present paper. The first one is spelled out in the title, and is inspired by an attempt to find an analogue of Hersch-Yang-Yau estimate for $lambda_1$ of surfaces in symplectic category. In particular we prove…