Branched covers of hyperbolic manifolds and harmonic maps

Branched Covers of Hyperbolic Manifolds and Harmonic Maps

Let f : M → N be a homotopy equivalence between closed negatively curved manifolds. The fundamental existence results of Eells and Sampson [5] and uniqueness of Hartmann [15] and Al’ber [1] grant the existence of a unique harmonic map h homotopic to f . Based on the enormous success of the harmonic map technique Lawson and Yau conjectured that the harmonic map h should be a diffeomorphism. This...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

stable exponentially harmonic maps between finsler manifolds

Hyperbolic Structures on Branched Covers over Hyperbolic Links

Using a result of Tian concerning deformation of negatively curved metrics to Einstein metrics, we conclude that, for any fixed link with hyperbolic complement, there is a class of irregular branched covering spaces, branched over that link, effectively detectable by their branching indices, which consists entirely of closed hyperbolic manifolds. Section 0 Introduction. One of the elusive compo...

Harmonic Maps on Kenmotsu Manifolds

We study in this paper harmonic maps and harmonic morphisms on Kenmotsu manifolds. We also give some results on the spectral theory of a harmonic map for which the target manifold is a Kenmotsu manifold.