Related papers: Flexible Lagrangians

The paths on the {\bf R$^3$} real Euclidean manifold are defined as 2-dimensional simplicial strips; points are replaced by 2-simplexes and the orbits of the action of a one discrete-parameter group on the base manifold becomes a convex…

We prove that Lagrangian cocores and Lagrangian linking disks of a stopped Weinstein manifold generate the Lagrangian cobordism infinity-category. As a geometric consequence, we see that any brane (after stabilization) admits a Lagrangian…

We study Legendrian embeddings of a compact Legendrian submanifold $L$ sitting in a closed contact manifold $(M,\xi)$ whose contact structure is supported by a (contact) open book $\mathcal{OB}$ on $M$. We prove that if $\mathcal{OB}$ has…

Via considerations of symplectic reduction, monodromy, mirror symmetry and Chern-Simons functionals, a conjecture is proposed on the existence of special Lagrangians in the hamiltonian deformation class of a given Lagrangian submanifold of…

Using the microlocal theory of sheaves, we associate a category to each Weinstein manifold. By constructing a microlocal specialization functor, we show that exact Lagrangians give objects in our category, and that the category is invariant…

We consider Riemannian metrics compatible with the natural symplectic structure on T^2 x M, where T^2 is a symplectic 2-Torus and M is a closed symplectic manifold. To each such metric we attach the corresponding Laplacian and consider its…

Let $X$ be a Weinstein manifold with ideal contact boundary $Y$. If $\Lambda\subset Y$ is a link of Legendrian spheres in $Y$ then by attaching Weinstein handles to $X$ along $\Lambda$ we get a Weinstein cobordism $X_{\Lambda}$ with a…

We give a complete characterization of those disk bundles over surfaces which embed as rationally convex strictly pseudoconvex domains in $\mathbb{C}^2$. We recall some classical obstructions and prove some deeper ones related to symplectic…

We investigate an equivalence relation on Legendrian knots in the standard contact three-space defined by the existence of an interpolating zigzag of Lagrangian cobordisms. We compare this relation, restricted to genus-$0$ surfaces, to…

We exhibit infinitely many, explicit special Lagrangian isolated singularities that admit no asymptotically conical special Lagrangian smoothings. The existence/ nonexistence of such smoothings is an important component of the current…

A Lagrangian study of two-dimensional turbulence for two different geometries, a periodic and a confined circular geometry, is presented to investigate the influence of solid boundaries on the Lagrangian dynamics. It is found that the…

We discuss some geometrical properties of the underlying N=2 geometry which encompasses some low--energy aspects of N=1 orientifolds as well as four dimensional N=2 Lagrangians including bulk and open string moduli.In the former case we…

By estimating the weighted volume, we obtain the optimal volume growth for Legendrian self-shrinkers. This, in turn, yields a rigidity theorem for entire smooth Legendrian self-shrinkers in the standard contact Euclidean (2n+1)-space.

We prove that any Legendrian knot in $(S^3,\xi_{std})$ bounds an exact Lagrangian surface in $\mathbb{R}^4\setminus B^4$ after a sufficient number of stabilizations. In order to show this, we construct a family combinatorial moves on knot…

A comparative analysis of two different versions of the Legendre transformation is presented. We provide an almost complete although somewhat superficial review of the geometric background for analytical mechanics. Complete coordinate…

The Universal Field Equations, recently constructed as examples of higher dimensional dynamical systems which admit an infinity of inequivalent Lagrangians are shown to be linearised by a Legendre transformation. This establishes the…

We formulate $\mathcal{N}=2$ global supersymmetric Lagrangians of self-interacting vector multiplets in terms of variant multiplets, whose non-propagating fields are replaced with gauge three-forms. Setting the three-forms on-shell results…

For a certain class of exotic contact manifolds of dimension greater than 3, we show that there is an abundance of closed exact Lagrangians in their symplectization. All of these Lagrangians are displaceable by Hamiltonian isotopy, and many…

We present new families of examples of non-simple prime Legendrian and transversal knots in tight Lens spaces, which demonstrate that the botany of Legendrians in Lens space is rich. In fact, there are more non-isotopic Legendrians that are…

In this note we construct augmentations of Chekanov-Eliashberg algebras of certain high dimensional Legendrian submanifolds that are not induced by exact Lagrangian fillings. The obstructions to the existence of exact Lagrangian fillings…