https://neckpinch.com/authors/jiazhuo-yang/New arXiv papers by Jiazhuo Yang, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.31023arxiv:2609.31023Fri, 25 Sep 2026 00:00:00 GMTHongyi Sheng, Weimin Sheng, Jiazhuo Yang — Let S^n+1_+ be the open hemisphere of the unit sphere S^n+1 centred at o. We study the non-homogeneous curvature flow X_t=-f(r) sigma_k^alpha nu of smooth, closed, strictly convex hypersurfaces enclosing o, where r is the geodesic distance to o. We consider both the supercritical regime beta>1+k alpha and the critical regime beta=1+kalpha, where beta is the growth order of the profile at the origin, f(r) almost equals r^beta as r descends to 0. Under the structural condition that f^{1/(1+kalpha)} is convex, we prove long-time existence and preservation of strict convexity. The normalized radial function converges smoothly and exponentially to a constant: to 1 and to R_infty>0, resp. in different two cases. Thus the normalized radial graphs become round, while the original hypersurfaces contract to o.Other curvature flowsHomogeneous spacesLong-time existence & convergence https://arxiv.org/abs/2609.29199arxiv:2609.29199Thu, 24 Sep 2026 00:00:00 GMTHongyi Sheng, Weimin Sheng, Jiazhuo Yang — Let H^n+1 be hyperbolic space of sectional curvature -1, with a fixed point o. We study the non-homogeneous curvature flow X_t=-f(r) sigma_k^alpha nu of smooth, closed, strictly h-convex hypersurfaces enclosing o, where r is the geodesic distance to o and alpha>0. The radial weight f is modeled on sinh^betar; we treat both regimes: beta>1+kalpha and beta=1+kalpha. Under a structural condition of f, the flow exists smoothly for all time, preserves strict h-convexity, and contracts to o. The normalized radial function converges, exponentially in normalized time: to 1 and to a positive constant R_infty respectively in two different cases.Other curvature flowsHomogeneous spaces https://arxiv.org/abs/2508.07361arxiv:2508.07361Sun, 10 Aug 2025 00:00:00 GMTWeimin Sheng, Jiazhuo Yang — In this paper, we study a class of non-homogeneous anisotropic fully nonlinear curvature flows in ℝⁿ⁺¹. More precisely, we consider a hypersurface M in ℝⁿ⁺¹ deformed by a flow along its unit normal with its speed f(r)σₖ^α where σₖ is the k-th elementary symmetric polynomial of M's principle curvatures, r is the distance of the point on M to the origin, f is a smooth nonnegative function on [0,∞) and α> 0. Under some suitable conditions on f, we prove that starting from a star-shaped and k-convex hypersurface, the flow exists for all time and converges smoothly to a sphere after normalization. In particular, we generalize the results in.Other curvature flowsHomogeneous spacesLong-time existence & convergence