ABSTRACT
Chapter 3
The Curvature-Eikonal
Flow for Convex Curves
In this chapter, we shall study the anisotropic curvature-eikonal ow
(ACEF) for closed convex curves. Three cases|contracting to a
point, converging to a stationary shape, and expanding to innity{
will be studied in detail in Sections 4, 5 and 6. In Section 3, we
present a self-contained treatment of an important special case|
the curve shortening ow. Some suÆcient conditions which ensure
shrinking to a point are established in Section 2. They apply to ows
more general than the ACEF and will be used in later chapters.
