Quasiconformal Harmonic Maps into Negatively Curved Manifolds

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Quasiisometries between negatively curved Hadamard manifolds

Let H1, H2 be the universal covers of two compact Riemannian manifolds (of dimension 6= 4) with negative sectional curvature. Then every quasiisometry between them lies at a finite distance from a bilipschitz homeomorphism. As a consequence, every self quasiconformal map of a Heisenberg group (equipped with the Carnot metric and viewed as the ideal boundary of complex hyperbolic space) of dimen...

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...

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-...

2 00 4 L 2 - cohomology of negatively curved Kähler manifolds of finite volume

We compute the space of L 2 harmonic forms (outside the middle degrees) on negatively curved Kähler manifolds of finite volume.