In this paper, we define an -Yang-Mills functional, and hence -Yang-Mills fields. The first and the second variational formulas are calculated, and the stabilities of -Yang-Mills fields on some submanifolds of the Euclidean spaces and the spheres are investigated, and hence the theories of Yang-Mills fields are generalized in this paper.
The linearized stability of stationary solutions for the surface diffusion flow with a triple junction is studied. We derive the second variation of the energy functional under the constraint that the enclosed areas are preserved and show a linearized stability criterion with the help of the -gradient flow structure of the evolution problem and the analysis of eigenvalues of a corresponding differential operator.
We show stability and consistency of the linear semi-implicit complementary volume numerical scheme for solving the regularized, in the sense of Evans and Spruck, mean curvature flow equation in the level set formulation. The numerical method is based on the finite volume methodology using the so-called complementary volumes to a finite element triangulation. The scheme gives the solution in an efficient and unconditionally stable way.
In this paper we firstly define a tangential Lichnerowicz cohomology on foliated manifolds. Next, we define tangential locally conformal symplectic forms on a foliated manifold and we formulate and prove some results concerning their stability.
We study the stability of the geodesic flow as a critical point for the energy functional when the base space is a compact orientable quotient of a two-point homogeneous space.
We prove the existence of many constant mean curvature surfaces of revolution with two ends which are immersed or embedded in hyperbolic space. We also study their stability.
On a -dimensional compact symplectic manifold, we consider a smooth family of compatible almost-complex structures such that at time zero the induced metric is Hermite-Einstein almost-Kähler metric with zero or negative Hermitian scalar curvature. We prove, under certain hypothesis, the existence of a smooth family of compatible almost-complex structures, diffeomorphic at each time to the initial one, and inducing constant Hermitian scalar curvature metrics.
A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M. We show that the moduli space of anti-self-dual connections on E is also hypercomplex, and admits a strong HKT metric. We also study manifolds with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of strong HKT-structures that have opposite...