Related papers: Stabilized symplectic embeddings of higher-dimensi…
The aim of this paper is to extend the coisotropic embedding theorem obtained by M. J. Gotay for pre-symplectic manifolds to more general geometric settings: cosymplectic, contact, cocontact, $k$-symplectic, $k$-cosymplectic, $k$-contact,…
We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore their certain difference…
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 discuss symplectic manifolds where, locally, the structure is that encountered in Lagrangian dynamics. Exemples and characteristic properties are given. Then, we refer to the computation of the Maslov classes of a Lagrangian submanifold.…
This paper analyzes circulant Johnson-Lindenstrauss (JL) embeddings which, as an important class of structured random JL embeddings, are formed by randomizing the column signs of a circulant matrix generated by a random vector. With the…
In this work we consider higher dimensional thin domains with the property that both boundaries, bottom and top, present oscillations of weak type. We consider the Laplace operator with Neumann boundary conditions and analyze the behavior…
Symplectic flux measures the areas of cylinders swept in the process of a Lagrangian isotopy. We study flux via a numerical invariant of a Lagrangian submanifold that we define using its Fukaya algebra. The main geometric feature of the…
We analyze tensors in the tensor product of three m-dimensional vector spaces satisfying Strassen's equations for border rank m. Results include: two purely geometric characterizations of the Coppersmith-Winograd tensor, a reduction to the…
Measure-theoretic slow entropy is a more refined invariant than the classical measure-theoretic entropy to characterize the complexity of dynamical systems with subexponential growth rates of distinguishable orbit types. In this paper we…
We investigate the ramifications of the Legendrian satellite construction on the relation of Lagrangian cobordism between Legendrian knots. Under a simple hypothesis, we construct a Lagrangian concordance between two Legendrian satellites…
Several results in recent years have shown that the usual generalizations of taut foliations to higher dimensions, based only on topological concepts, lead to a theory that lacks the complexity of its 3-dimensional counterpart. Instead, we…
We establish new upper bounds for the height of the S-integral points of an elliptic curve. This bound is explicitly given in terms of the set S of places of the number field K involved, but also in terms of the degree of K, as well as the…
We prove a tubular neighborhood theorem for an embedded complex geodesic surface in a complex hyperbolic 2-manifold where the width of the tube depends only on the Euler characteristic of the embedded surface. We give an explicit estimate…
The study of (minimally) rigid graphs is motivated by numerous applications, mostly in robotics and bioinformatics. A major open problem concerns the number of embeddings of such graphs, up to rigid motions, in Euclidean space. We capture…
We consider linearly stable elliptic fixed points for a symplectic vector field and prove generic results of super-exponential stability for nearby solutions. Morbidelli and Giorgilli have proved a theorem of stability over…
We present a generalized Weinstein Tubular Neighbourhood theorem for Lagrangian subbundles of Symplectic fibrations. This is then used to study the space of Lagrangian fibrations of symplectic manifolds.
We study integration and $L_2$-approximation on countable tensor products of function spaces of increasing smoothness. We obtain upper and lower bounds for the minimal errors, which are sharp in many cases including, e.g., Korobov, Walsh,…
Let $X$ be an $n$-dimensional smooth complex projective variety embedded in $\mathbb{C}\mathbb{P}^{N}$. We construct a smooth family $\mathcal{X}$ over $\mathbb{C}$ with an embedding in $\mathbb{C}\mathbb{P}^{N} \times \mathbb{C}$ whose…
We study the ellipticity and the ``Nekhoroshev stability'' (stability properties for finite, but very long, time scales) of the Riemann ellipsoids. We provide numerical evidence that the regions of ellipticity of the ellipsoids of types II…
We investigate the Hilbert complex of elasticity involving spaces of symmetric tensor fields. For the involved tensor fields and operators we show closed ranges, Friedrichs/Poincare type estimates, Helmholtz type decompositions, regular…