Quasiconformal harmonic maps into negatively curved manifolds

Donnelly, Harold

Illinois J. Math., Tome 45 (2001) no. 4, p. 603-613 / Harvested from Project Euclid

Résumé

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.

Publié le : 2001-04-15
Classification: 58E20, 53C43

@article{1258138358,
     author = {Donnelly, Harold},
     title = {Quasiconformal harmonic maps into negatively curved manifolds},
     journal = {Illinois J. Math.},
     volume = {45},
     number = {4},
     year = {2001},
     pages = { 603-613},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138358}
}

Donnelly, Harold. Quasiconformal harmonic maps into negatively curved manifolds. Illinois J. Math., Tome 45 (2001) no. 4, pp.  603-613. http://gdmltest.u-ga.fr/item/1258138358/