Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-25T14:55:15.696Z Has data issue: false hasContentIssue false
  • English
  • Français

Evolution of non-simple closed curves in the area-preserving curvature flow

Part of: Partial differential equations Parabolic equations and systems Global differential geometry

Published online by Cambridge University Press:  28 December 2017

Xiao-Liu Wang ,
Wei-Feng Wo  and
Ming Yang
Xiao-Liu Wang
Affiliation:
School of Mathematics, Southeast University, Nanjing 210096, People's Republic of China ([email protected])
Wei-Feng Wo
Affiliation:
Department of Mathematics, Ningbo University, Ningbo 315211, People's Republic of China
Ming Yang
Affiliation:
School of Mathematics, Southeast University, Nanjing 210096, People's Republic of China
Get access Rights & Permissions [Opens in a new window]

Abstract

The convergence and blow-up results are established for the evolution of non-simple closed curves in an area-preserving curvature flow. It is shown that the global solution starting from a locally convex curve converges to an m-fold circle if the enclosed algebraic area A0 is positive, and evolves into a point if A0 = 0.

Keywords

curvature flownon-localblow-upconvergence

MSC classification

Secondary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.) 35B40: Asymptotic behavior of solutions 35K59: Quasilinear parabolic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 3 , June 2018 , pp. 659 - 668
Copyright
Copyright © Royal Society of Edinburgh 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)