Illinois Journal of Mathematics

Quasiconformal harmonic maps into negatively curved manifolds

Harold Donnelly

Abstract

Let $F:M\to N$ 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 of bounded dilation is constant.

Article information

Source
Illinois J. Math., Volume 45, Number 2 (2001), 603-613.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138358

Digital Object Identifier
doi:10.1215/ijm/1258138358

Mathematical Reviews number (MathSciNet)
MR1878621

Zentralblatt MATH identifier
0993.58012

Citation

Donnelly, Harold. Quasiconformal harmonic maps into negatively curved manifolds. Illinois J. Math. 45 (2001), no. 2, 603--613. doi:10.1215/ijm/1258138358. https://projecteuclid.org/euclid.ijm/1258138358