Curve Shortening Flow in Arbitrary Dimensional Euclidian Space

Authors
Yang, Yun Yan Jiao, Xiao Xiang
Citation
Yang, Yun Yan et Jiao, Xiao Xiang, Curve Shortening Flow in Arbitrary Dimensional Euclidian Space, Acta mathematica Sinica. English series (Print) , 21(4), 2005, pp. 715-722
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
21
Issue
4
Year of publication
2005
Pages
715 - 722
Database
ACNP
SICI code
Abstract
In this paper, curve shortening flow in Euclidian space R n(n 3) is studied, and S. Altschulers results about flow for space curves are generalized. We prove that the curve shortening flow converges to a straight line in infinite time if the initial curve is a ramp. We also prove the planar phenomenon when the curve shortening flow blows up.