Lemm, Marius and Markovic, Vladimir (2018) Heat flows on hyperbolic spaces. Journal of Differential Geometry, 108 (3). pp. 495-529. ISSN 0022-040X. doi:10.4310/jdg/1519959624. https://resolver.caltech.edu/CaltechAUTHORS:20170508-064511268
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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 S^(n−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 S^(n−1), n ≥ 3, can be extended to a harmonic quasi-isometry of the n-dimensional hyperbolic space.
Item Type: | Article | ||||||||||||
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Additional Information: | © 2018 International Press. Received November 14, 2015. Vladimir Markovic is supported by the NSF grant number DMS-1500951. | ||||||||||||
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Issue or Number: | 3 | ||||||||||||
DOI: | 10.4310/jdg/1519959624 | ||||||||||||
Record Number: | CaltechAUTHORS:20170508-064511268 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170508-064511268 | ||||||||||||
Official Citation: | Lemm, Marius; Markovic, Vladimir. Heat flows on hyperbolic spaces. J. Differential Geom. 108 (2018), no. 3, 495--529. doi:10.4310/jdg/1519959624. https://projecteuclid.org/euclid.jdg/1519959624 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 77246 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Ruth Sustaita | ||||||||||||
Deposited On: | 12 May 2017 23:49 | ||||||||||||
Last Modified: | 15 Nov 2021 17:29 |
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