Paper · Sep 21, 2026
Anisotropic-Length-Preserving Weighted Anisotropic Curvature Flows
As on arXiv
Abstract
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.
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
-
On length-preserving and area-preserving inverse curvature flows in the hyperbolic plane
Topics Long-time existence & convergence, Other curvature flows · Same authors Zhishuai Liu, Guoxin Wei · Shared terms “length preserving”, “converges smoothly”, “flow exists”
-
Some aspects of anisotropic curvature flow of planar partitions
Topics Anisotropic & nonlocal flows, Other curvature flows
-
Type-II Singularities of Immersed Locally Convex Curves Evolving under Generalized Anisotropic Gage Area-Preserving Flows with Slow Curvature Speeds
Topics Anisotropic & nonlocal flows, Other curvature flows · Shared terms “anisotropic length”, “initial curves”, “closed plane”
-
Area-Preserving Anisotropic Mean Curvature Flow in Two Dimensions
Topics Anisotropic & nonlocal flows, Long-time existence & convergence · Shared terms “Wulff shape”
-
A flow method for a generalization of Christofell-Minkowski problem
Topics Anisotropic & nonlocal flows, Long-time existence & convergence, Other curvature flows
-
Anisotropic Gauss curvature flow of complete non-compact graphs
Topics Anisotropic & nonlocal flows, Long-time existence & convergence, Other curvature flows · Shared terms “Wulff shape”, “flow exists”
-
Deforming Locally Convex Curves into Curves of Constant -order Width
Topics Anisotropic & nonlocal flows, Long-time existence & convergence, Other curvature flows
-
Minimizing movements for forced anisotropic curvature flow of droplets
Topics Anisotropic & nonlocal flows, Other curvature flows
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.