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research article
Heat flows on hyperbolic spaces
March 1, 2018
In this paper we develop new methods for studying the convergence problem for the heat flow on negatively curved spaces and prove that any quasiconformal map of the sphere Sn−1,n≥3, can be extended to the n-dimensional hyperbolic space such that the heat flow starting with this extension converges to a quasi-isometric harmonic map. This implies the Schoen–Li–Wang conjecture that every quasiconformal map of Sn−1,n≥3, can be extended to a harmonic quasi-isometry of the n-dimensional hyperbolic space.
Type
research article
Authors
Publication date
2018-03-01
Published in
Volume
108
Issue
3
Start page
495
End page
529
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
October 1, 2020
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