Energy identity for harmonic maps into standard stationary Lorentzian manifolds

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Quasiconformal Harmonic Maps into Negatively Curved Manifolds

Let F : M → N be a harmonic map between complete Riemannian manifolds. Assume that N is simply connected with sectional curvature bounded between two negative constants. If F is a quasiconformal harmonic diffeomorphism, then M supports an infinite dimensional space of bounded harmonic functions. On the other hand, if M supports no non-constant bounded harmonic functions, then any harmonic map o...

stable exponentially harmonic maps between finsler manifolds

Periodic trajectories on stationary Lorentzian manifolds

In this paper we present an existence and multiplicity result for periodic trajectories on stationary Lorentzian manifolds, possibly with boundary, whose proof is based on a Morse theory approach, see [5]. We recall that a Lorentzian manifold is a smooth connected nite-dimensional manifold M equipped with a (0; 2) tensor eld g such that for any z ∈ M g(z) [·; ·] is a nondegenerate symmetric bil...

Harmonic fields on mixed Riemannian-Lorentzian manifolds

The extended projective disc is Riemannian at ordinary points, Lorentzian at ideal points, and singular on the absolute. Harmonic fields on this metric can be interpreted as the hodograph image of extremal surfaces in Minkowski 3-space. This suggests an approach to generalized Plateau problems in 3-dimensional space-time via Hodge theory on the extended projective disc. Boundary-value problems ...