https://neckpinch.com/authors/zhishuai-liu/New arXiv papers by Zhishuai Liu, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2609.24431/arxiv:2609.24431Mon, 21 Sep 2026 00:00:00 GMTZhishuai Liu, Guoxin Wei — In this paper, we study the anisotropic-length-preserving weighted anisotropic curvature flow for smooth convex closed plane curves. For any smooth, embedded, closed, convex initial curve, the flow exists smoothly for all time, and the anisotropic curvature converges smoothly to that of the boundary of the corresponding homothetic Wulff shape as time tends to infinity.Other curvature flowsAnisotropic & nonlocal flowsLong-time existence & convergence https://neckpinch.com/papers/2604.11443/arxiv:2604.11443Mon, 13 Apr 2026 00:00:00 GMTZhishuai Liu, Guoxin Wei — In this paper, we study the area-preserving and length-preserving κ^α-type curvature flows of smooth, closed, convex curves in the two-dimensional hyperbolic plane ℍ² for α<0 and prove that convexity is preserved along the flows. Assuming that the flows exist for all time, we show that the evolving curves converge smoothly to geodesic circles. Furthermore, we also derive a sufficient condition for global existence of the flows.Other curvature flowsInverse mean curvature flowVolume-preserving & constrained flowsSurfacesLong-time existence & convergence