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Quasiconformal mappings and manifolds of negative curvature. (English) Zbl 0592.53031
Curvature and topology of Riemannian manifolds, Proc. 17th Int. Taniguchi Symp., Katata/Jap. 1985, Lect. Notes Math. 1201, 212-229 (1986).
[For the entire collection see Zbl 0583.00022.]
First, the author is concerned with a generalization of Schwarz’ lemma which shows that a quasiconformal mapping f between manifolds of bounded negative curvature is a quasiisometry. Then he obtains some capacity estimates and proves that locally symmetric spaces do not admit very pinched metrics. Finally, one shows that one can speak of conformal and quasiconformal mappings on the boundary of a manifold of negative curvature as soon as there is a cocompact isometry group.
Reviewer: A.Bejancu

MSC:
53C20 Global Riemannian geometry, including pinching
30C62 Quasiconformal mappings in the complex plane
30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination