Heat flows on hyperbolic spaces

Author: 

Lemm, M
Markovic, V

Publication Date: 

2 March 2018

Journal: 

Journal of Differential Geometry

Last Updated: 

2021-01-10T14:19:13.183+00:00

Issue: 

3

Volume: 

108

DOI: 

10.4310/jdg/1519959624

page: 

495-529

abstract: 

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.

Symplectic id: 

1109985

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article