Harmonic maps into hyperbolic $3$-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...

Harmonic Maps between 3 - Dimensional Hyperbolic Spaces

We prove that a quasiconformal map of the sphere S admits a harmonic quasi-isometric extension to the hyperbolic space H, thus confirming the well known Schoen Conjecture in dimension 3.

stable exponentially harmonic maps between finsler manifolds

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...