https://neckpinch.com/authors/xuezhang-chen/New arXiv papers by Xuezhang Chen, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1906.08434/arxiv:1906.08434Thu, 20 Jun 2019 00:00:00 GMTXuezhang Chen, Pak Tung Ho — We study a fractional conformal curvature flow on the standard unit sphere and prove a perturbation result of the fractional Nirenberg problem with fractional exponent σ∈ (1/2,1). This extends the result of Chen-Xu (Invent. Math. 187, no. 2, 395-506, 2012) for the scalar curvature flow on the standard unit sphere.Other curvature flowsScalar curvature https://neckpinch.com/papers/1605.01719/arxiv:1605.01719Thu, 05 May 2016 00:00:00 GMTXuezhang Chen, Pak Tung Ho, Liming Sun — We employ three different methods to prove the following result on prescribed scalar curvature plus mean curvature problem: Let (Mⁿ,g₀) be a n-dimensional smooth compact manifold with boundary, where n ≥ 3, assume the conformal invariant Y(M,∂M)<0. Given any negative smooth functions f in M and h on ∂M, there exists a unique conformal metric of g₀ such that its scalar curvature equals f and mean curvature curvature equals h. The first two methods are sub-super-solution method and subcritical approximation, and the third method is a geometric flow. In the flow approach, assume another conformal invariant Q(M,pa M) is a negative real number, for some class of initial data, we prove the short time and long time existences of the so-called prescribed scalar curvature plus mean curvature flows, as well as their asymptotic convergence. Via a family of such flows together with some additional variational arguments, under the flow assumptions we prove existence and uniqueness of positive minimizers of the associated energy functional and also the above result by analyzing asymptotic limits of the flows and the relations among some conformal invariants.Mean curvature flowScalar curvatureStability & uniquenessBoundaries & non-compactLong-time existence & convergence