ABSTRACT
Theorem 5.1 (Grayson convexity theorem) Consider the CSF
where
is a smooth, embedded closed curve. There exists a t
< !
such that (; t) is uniformly convex for all t 2 [t
; !).
The proof of this theorem is based on the monotoncity of an
isoperimetric ratio introduced by Hamilton (Section 1) and a blow-
up argument (Section 2). Next, we discuss the classication of the
singularities of the CSF for immersed curves in Section 3.
