In the past few years there have been several striking results about the topology of Lagrangian surfaces in symplectic four-manifolds. The general tendency of these results is that many isotopy classes of embedded surfaces do not contain Lagrangian representatives. This is called the topological unknottedness of Lagrangian surfaces; see [4] for a survey. The aim of this paper is to complement t...

This paper introduces a geometrically constrained variational problem for the area functional. We consider the area restricted to the lagrangian surfaces of a Kähler surface, or, more generally, a symplectic 4-manifold with suitable metric, and study its critical points and in particular its minimizers. We apply this study to the problem of finding canonical representatives of the lagrangian ho...

In this paper we show how to lift Lagrangian immersions in $\mathbb{C} P^{n-1}$ produce cones ^n$, and use process several families of examples special cones. Moreover cones, isotopic the Harvey-Lawson trivial whose projections are with few transverse double points.

We study singularities of Lagrangian mean curvature flow in C when the initial condition is a zero-Maslov class Lagrangian. We start by showing that, in this setting, singularities are unavoidable. More precisely, we construct Lagrangians with arbitrarily small Lagrangian angle and Lagrangians which are Hamiltonian isotopic to a plane that, nevertheless, develop finite time singularities under ...

Anomalous sector of chiral Lagrangian is calculated in a gauge invariant, nonlocal, dynamical quark model. The Wess-Zumino term is proved coming from two kinds of sources, one is independent of and another dependent on dynamical quark self energy Σ(k2). p6 and more higher order anomalous sectors come only from Σ(k2) dependent source. After some cancellation, standard Wess-Zumino action is obtai...

We consider a connected symplectic manifold M acted on properly and in a Hamiltonian fashion by a connected Lie group G. Inspired to the recent paper [3], see also [12] and [24], we study Lagrangian orbits of Hamiltonian actions. The dimension of the moduli space of the Lagrangian orbits is given and we also describe under which condition a Lagrangian orbit is isolated. If M is a compact Kähler...

Abstract Furuta pendulum is an underdriven and unstable controlled object with one input two outputs, has open-loop zero point at the origin of complex plane. In this paper, a nonlinear dynamic model established by Eulerian-Lagrangian method, series-connected PID control strategy designed using root locus method frequency domain analysis based on local linearization steady-state operating point...