Bounded harmonic maps
The classical Fatou theorem identifies bounded harmonic functions on the unit disk with bounded measurable functions on the boundary circle. We extend this theorem to bounded harmonic maps.
math.DG↗
arXiv subjects
Dominique Hulin
Publications and source records attributed to Dominique Hulin.
Harmonic quasi-isometries of pinched Hadamard surfaces are injective
We prove that a harmonic quasi-isometric map between pinched Hadamard surfaces is a quasi-conformal diffeomorphism.
math.DG↗
Harmonic quasi-isometric maps III :quotients of Hadamard manifolds
In a previous paper, we proved that a quasi-isometric map $f:X\longrightarrow Y$ between two pinched Hadamard manifolds $X$ and $Y$ is within bounded distance from a unique harmonic map. We extend this result to maps $f:Γ\backslash X\longrightarrow Y$, where $Γ$ is a convex cocompact discrete group of isometries of $X$ and $f$ is locally quasi-isometric at infinity.
math.DG↗
Harmonic quasi-isometric maps II : negatively curved manifolds
We prove that a quasi-isometric map, and more generally a coarse embedding, between pinched Hadamard manifolds is within bounded distance from a unique harmonic map.
math.DG↗
Quasiisometric harmonic maps between rank one symmetric spaces
We prove that a quasiisometric map between rank one symmetric spaces is within bounded distance from a unique harmonic map. In particular, this completes the proof of the Schoen-Li-Wang conjecture.
math.DG↗