Related papers: Complete lagrangian self-expanders in $\mathbb C^{…

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…

We define the notion of special Lagrangian curvature, showing how it may be interpreted as an alternative higher dimensional generalisation of two dimensional Gaussian curvature. We obtain first a local rigidity result for this curvature…

We describe the structure of all continuous Jordan triple endomorphisms of the set $\mathbb{P}_2$ of all positive definite $2\times 2$ matrices thus completing a recent result of ours. We also mention an application concerning sorts of…

In this work, we study Lagrangian formulations for self-dual gauge theories, also known as chiral $n$-form gauge theories, for $n = 2p$ in $D = 4p+2$ dimensional spacetime. Motivated by a recent formulation of M5-branes derived from the BLG…

We complete the list of normal forms for effective 3-forms with constant coefficients with respect to the natural action of symplectomorphisms in \mathbb{R}^6. We show that the 3-form which corresponds to the Special Lagrangian equation is…

This article presents a comprehensive overview and supplement to recent developments in second-order elliptic partial differential equations formulated in double divergence form, along with an exploration of their parabolic counterparts.

An algebra extension $A \| B$ is right depth two in this paper if its tensor-square is $A$-$B$-isomorphic to a direct summand of any (not necessarily finite) direct sum of $A$ with itself. For example, normal subgroups of infinite groups,…

We study geometric properties of complete non-compact bounded self-shrinkers and obtain natural restrictions that force these hypersurfaces to be compact. Furthermore, we observe that, to a certain extent, complete self-shrinkers intersect…

We provide in this note two relevant examples of Lagrangian cobordisms. The first one gives an example of two exact Lagrangian submanifolds which cannot be composed in an exact fashion. The second one is an example of an exact Lagrangian…

The existence of a Lagrangian description for the second-order Riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized Riccati equation. The Lagrangians are…

$\lambda$-self-expanders $\Sigma$ in $\mathbb{R}^{n+1}$ are the solutions of the isoperimetric problem with respect to the same weighted area form as in the study of the self-expanders. In this paper, we mainly extend the results on…

In this paper we consider minimal Lagrangian submanifolds in $n$-dimensional complex space forms. More precisely, we study such submanifolds which, endowed with the induced metrics, write as a Riemannian product of two Riemannian manifolds,…

We prove a new lower bound for the exponent of growth of the best two-dimensional Diophantine approximations with respect to Euclidean norm.

We prove an existence result for exact lagrangian cobordisms between closed legendrians.

Let X be a 2-dimensional simplicial complex. The degree of an edge e is the number of 2-faces of X containing e. The complex X is an \epsilon-expander if the coboundary d_1(\phi) of every Z_2-valued 1-cochain \phi \in C^1(X;Z_2) satisfies…

We prove extension of a di-bar-closed, smooth, form from the intersection of a pseudoconvex domain with a complex hyperplane to the whole domain. The extension form is di-bar-closed, has harmonic coefficients and its L^2-norm is estimated…

We study Hamiltonian stationary Lagrangian surfaces in C^2, i.e. Lagrangian surfaces in C^2 which are stationary points of the area functional under smooth Hamiltonian variations. Using loop groups, we propose a formulation of the equation…

In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…

Let $(M,\bar g)$ be a compact Riemannian manifold with minimal boundary such that the second fundamental form is nowhere vanishing on $\partial M$. We show that for a generic Riemannian metric $\bar g$, the squared norm of the second…

In this paper, we give a complete classification of symplectic structures on six-dimensional Frobeniusian solvable Lie algebras, up to symplectomorphism. We provide a scheme to classify the isomorphism classes of six-dimensional…