Stability of commuting maps and Lie maps

Stability of F-biharmonic maps

This paper studies some properties of F-biharmonic maps between Riemannian manifolds. By considering the first variation formula of the F-bienergy functional, F-biharmonicity of conformal maps are investigated. Moreover, the second variation formula for F-biharmonic maps is obtained. As an application, instability and nonexistence theorems for F-biharmonic maps are given.

Commuting Dual Billiard Maps

Abstract. To a closed convex smooth curve in the plane the dual billiard transformation of its exterior corresponds: given a point outside of the curve, draw a tangent line to it through the point, and reflect the point in the point of tangency. We prove that if two curves are given, such that the corresponding dual billiard transformations commute, then the curves are concentric hornothetic el...

Canonical Metrics of Commuting Maps

Let φ : X → X be a map on an projective variety. It is known that whenever φ∗ : Pic(X) ⊗ R → Pic(X) ⊗ R has an eigenvalue α > 1, we can build a canonical measure, a canonical height and a canonical metric associated to φ. In the present work, we establish the following fact: if two commuting maps φ, ψ : X → X satisfy these conditions, for eigenvalues α and β and the same eigenvector L, then the...

Cq-COMMUTING MAPS AND INVARIANT APPROXIMATIONS

Let X be a linear space. A p-norm on X is a real-valued function on X with 0 < p ≤ 1, satisfying the following conditions: (i) ‖x‖p ≥ 0 and ‖x‖p = 0⇔ x = 0, (ii) ‖αx‖p = |α|p‖x‖p, (iii) ‖x+ y‖p ≤ ‖x‖p +‖y‖p, for all x, y ∈ X and all scalars α. The pair (X ,‖ · ‖p) is called a p-normed space. It is a metric linear space with a translation invariant metric dp defined by dp(x, y)= ‖x− y‖p for all ...

Commuting maps on rank-k matrices