https://neckpinch.com/authors/hong-zhang/New arXiv papers by Hong Zhang, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2105.00170/arxiv:2105.00170Sat, 01 May 2021 00:00:00 GMTPak Tung Ho, Quoc Anh Ngo, Hong Zhang — Using the prescribed Webster scalar curvature flow, we prove some existence results on the 3-dimensional compact CR manifold with nonnegative CR Yamabe constant.Other curvature flows3-manifoldsScalar curvature https://neckpinch.com/papers/1705.09627/arxiv:1705.09627Fri, 26 May 2017 00:00:00 GMTHong Zhang — In this paper, we consider the problem of prescribing scalar curvature on n-sphere. Assume that the candidate curvature function f, which is allowed to change sign, satisfies some kind of Morse index or symmetry condition. By studying the well-known scalar curvature flow, we are able to prove that the flow converges to a metric with the prescribed function f as its scalar curvature.Other curvature flowsScalar curvature https://neckpinch.com/papers/1701.02247/arxiv:1701.02247Mon, 09 Jan 2017 00:00:00 GMTQuôc Anh Ngô, Hong Zhang — On a closed Riemannian manifold (M,g₀) of even dimension n geqslant 4, the well-known prescribed Q-curvature problem asks whether or not there is a metric g comformal to g₀ such that its Q-curvature, associated with the GJMS operator mathbf P_g, is equal to a given function f. Letting g = e^(2u)g₀, this problem is equivalent to solving mathbf P_(g₀) u+Q_(g₀) = f e^(nu), where Q_(g₀) denotes the Q-curvature of g₀. The primary objective of the paper is to introduce the following negative gradient flow of the time dependent metric g(t) conformal to g₀, (∂g (t))/∂t= −2(Q_(g (t)) − frac∫_M f Q_(g(t)) dμ_(g(t)) ∫_M f² dμ_(g(t)) f )g(t) for t >0, to study the problem of prescribing Q-curvature. Since ∫_M Q_g dμ_g is conformally invariant, our analysis depends on the size of ∫_M Q_(g₀) dμ_(g₀), which is assumed to satisfy ∫_M Q₀ dμ_(g₀) ≠ k (n-1)! rm vol(Sⁿ) for all k = 2,3,... The paper is twofold. First, we identify suitable conditions on f such that the gradient flow defined as above is defined to all time and convergent, as time goes to infinity, sequentially or uniformly. Second, we show that various existence theorems for prescribed Q-curvature problem can be derived from the convergence of the flow.Other curvature flows