Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
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.
Evan Fair Johnson, Serdar Hiçdurmaz