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Heat flows on hyperbolic spaces

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.

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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.

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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
Record Number:CaltechAUTHORS:20170508-064511268
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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.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77246
Deposited By: Ruth Sustaita
Deposited On:12 May 2017 23:49
Last Modified:15 Nov 2021 17:29

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