https://neckpinch.com/authors/shijin-zhang/New arXiv papers by Shijin Zhang, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1906.00444/arxiv:1906.00444Sun, 02 Jun 2019 00:00:00 GMTShijin Zhang — In this short note, using Günther's volume comparison theorem and Yokota's gap theorem on complete shrinking gradient Ricci solitons, we prove that for any complete shrinking gradient Ricci soliton (Mⁿ,g,f) with sectional curvature K(g)<A and rm Vol_f(M)≥ v for some uniform constant A,v, there exists a small uniform constant ε_(n,A,v)>0 depends only on n, A and v, if the scalar curvature R≤ ε_(n,A,v), then (M,g,f) is isometric to the Gaussian soliton (ℝⁿ, g_E, frac|x|²4).Ricci solitonsScalar curvature https://neckpinch.com/papers/1906.00415/arxiv:1906.00415Sun, 02 Jun 2019 00:00:00 GMTShijin Zhang — In this paper, we prove that any complete shrinking gradient Kähler-Ricci solitons with positive orthogonal bisectional curvature must be compact. We also obtain a classification of the complete shrinking gradient Kähler-Ricci solitons with nonnegative orthogonal bisectional curvature.Ricci solitonsKähler–Ricci solitonsKähler geometry https://neckpinch.com/papers/1906.00412/arxiv:1906.00412Sun, 02 Jun 2019 00:00:00 GMTGuoqiang Wu, Shijin Zhang — In this short note, using an argument by Munteanu and Wang, we provide an alternative proof of the fact first obtained by Lei Ni that shrinking gradient Kähler-Ricci solitons with positive bisectional curvature must be compact.Ricci solitonsKähler–Ricci solitonsKähler geometry https://neckpinch.com/papers/1610.03366/arxiv:1610.03366Tue, 11 Oct 2016 00:00:00 GMTXin Fu, Shijin Zhang — We study the behavior of the Kähler-Ricci flow on some Fano bundle which is a trivial bundle on one Zariski open set. We show that if the fiber is ℙ^(m) blown up at one point or some weighted projective space blown up at the orbifold point and the initial metric is in a suitable kähler class, then the fibers collapse in finite time and the metrics converge sub-sequentially in Gromov-Hausdorff sense to a metric on the base.Ricci flowKähler–Ricci flowSingularitiesKähler geometryLimit spaces & RCD https://neckpinch.com/papers/1609.09806/arxiv:1609.09806Fri, 30 Sep 2016 00:00:00 GMTHuabin Ge, Shijin Zhang — We prove that there does not exist non-constant positive f-harmonic function on the complete gradient shrinking Ricci solitons. We also prove the L^(p)(p≥ 1 rm or 0<p≤ 1) Liouville theorems on the complete gradient shrinking Ricci solitons.Ricci solitons