Harmonic quasi-isometric maps II: negatively curved 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

Quasi-conformal Rigidity of Negatively Curved Three Manifolds

In this paper we study the rigidity of infinite volume 3-manifolds with sectional curvature −b2 ≤ K ≤ −1 and finitely generated fundamental group. In-particular, we generalize the Sullivan’s quasiconformal rigidity for finitely generated fundamental group with empty dissipative set to negative variable curvature 3-manifolds. We also generalize the rigidity of Hamenstädt or more recently Besson-...

Negatively Ricci Curved Manifolds

In this paper we announce the following result: “Every manifold of dimension ≥ 3 admits a complete negatively Ricci curved metric.” Furthermore we describe some sharper results and sketch proofs.

stable exponentially harmonic maps between finsler manifolds