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arXiv · 1506.04345

Heat flows on hyperbolic spaces

Marius Lemm·Vladimir Markovic
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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 $\mathbb{S}^{n-1}$, $n\geq 3$, 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.

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Marius Lemm, Vladimir Markovic. 2015-06-14. Heat flows on hyperbolic spaces. https://arxiv.org/abs/1506.04345

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