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March 2018 Heat flows on hyperbolic spaces
Marius Lemm, Vladimir Markovic
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J. Differential Geom. 108(3): 495-529 (March 2018). DOI: 10.4310/jdg/1519959624

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 $\mathbb{S}^{n-1} , n \geq 3$, 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 $\mathbb{S}^{n-1} , n \geq 3$, can be extended to a harmonic quasi-isometry of the $n$-dimensional hyperbolic space.

Funding Statement

Vladimir Markovic is supported by the NSF grant number DMS-1500951.

Citation

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Marius Lemm. Vladimir Markovic. "Heat flows on hyperbolic spaces." J. Differential Geom. 108 (3) 495 - 529, March 2018. https://doi.org/10.4310/jdg/1519959624

Information

Received: 14 November 2015; Published: March 2018
First available in Project Euclid: 2 March 2018

zbMATH: 06846984
MathSciNet: MR3770849
Digital Object Identifier: 10.4310/jdg/1519959624

Rights: Copyright © 2018 Lehigh University

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Vol.108 • No. 3 • March 2018
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