Curve Shortening Flow in Arbitrary Dimensional Euclidian Space

In this paper,curve shortening flow in Euclidian space R~n(n 3) is studied,and S.Altschuler’s results about flow for space curves are generalized.We prove that the curve shorteningflow converges to a straight line in infinite time if the initial curve is a ramp.We also prove the planarphenomenon when the curve shortening flow blows up.