https://neckpinch.com/authors/jie-xu/New arXiv papers by Jie Xu, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2002.02350/arxiv:2002.02350Thu, 06 Feb 2020 00:00:00 GMTJie 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 (2t/N · frac∂²∂t² + (tR(t, x))/N ∂/∂t − Δ_(g^((N))(t)) ) u = R(t, x) outside its wavefront set onto ℝₜ × M_(x, g(t)) solves the backward heat equation ∂ₜ u + Δ_(x, g(t)) u = −R(t, x) 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