We characterize microlocal ultradifferentiablity of a distribution in a maximally real submanifold of $\mathbb{C}^m$ using the FBI transform.

In this paper, the method of vanishing viscosity described by Evans [10] is used to prove, the existence and uniqueness theorems for the viscosity solution of the Vlasov equation in the presence of a Yang-Mills field in temporal gauge. Such equation governs the evolution without collisions of plasmas, for instance of quarks and gluons (quagmas), where non Abelian gauge fields and Yang-Mills charges replace the usual electromagnetic field and electric charges.

In this paper, we give the Cartan's formula for half-lightlike submanifolds of Lorentzian manifolds and use it to show that a screen homothetic half-lightlike submanifold of a Lorentzian space form, with a closed conformal co-screen distribution is locally a lightlike triple product manifold. Then we give a classification theorem for half-lightlike submanifolds of Lorentzian space form with constant screen principal curvatures. These results extend some ones obtained in the case of lightlike hypersurfaces of Lorentzian manifolds.

We study the intersection of closed geodesics in hyperbolic surfaces which admits a particular pair of pants decomposition. We prove under some assumptions that the angle of intersection is bounded from below and the length of closed geodesic is bounded from above.