Research profile

Jie Xu

Works on Poincaré conjecture and Ricci flow.

NP-RC-104980

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Poincaré conjectureRicci flow

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Their work in this field since 2016, with the older papers the site recommends. Titles open each paper's page, with its abstract, PDF and HTML versions; Connections shows the papers closest to it. The arXiv listing has the complete record.

2020

math.DGarXiv:2002.02350

Wave Approximation of Backward Heat Equation with Ricci Flow

Jie Xu

In this paper, we consider solutions of the backward heat equation with Ricci flow on manifolds as a type of infinite dimensional limit of solutions of a wave equation on a larger manifold with an analysis of wavefront set. Specifically, the projection of the solution of the wave equation outside its wavefront set onto solves the backward heat equation within some appropriate time interval. We discuss this approximation starting from Euclidean case, and then extend to the open Riemannian manifold situation. This idea partially comes from Perelman's original papers in proving Poincaré conjecture as well as Terence Tao's Notes in UCLA.

Ricci flowPoincaré conjecture
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A window on one part of a person's work: papers here go back to 2016 and cover Ricci flow and its neighbouring flows, with the older work the site recommends, so this page is no measure of anyone's whole output. Being listed is not an endorsement by or of the person. If two people share this name, their work may appear together here. How it is put together.